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PERKINS' SERIES 



PLANE TRIGONOMETRY 



AND ITS APPLICATION TO 



MENSURATION 



AND 



LAND SURVEYING 



ACCOMPANIED WITH ALL THE NECESSARY 



LOGARITHMIC AND TRIGONOMETRIC 



» g » c 



« a i 



TABLES. 



GEORGE R. PERKINS, A. M. 

PRINCIPAL AND PROFESSOR OF MATHEMATICS IN NEW YORK STATE NORMAL SCHOOL, 



l. 



?5 11- 



AUTHOR OF "ELEMENTARY ARITHMETIC, "HIGHER ARITHMETIC 
"ELEMENTS OF ALGEBRA," "practical 
GEOMETRY," ETC. 



NEW YORK: 
D. APPLETON & COMPANY, 200 BROADWAY. 



MDCCCLII. 



Entered according to Act of Congress, in the year 1851, 

By GEORGE R. PERKINS, 

in the Clerk's Office of the District Court for the Northern District of New York. 



PREFACE. 



In this work we have endeavored to make the whole as 
simple and practical as the nature of the different subjects 
would admit. The portion devoted to Land Surveying will 
be found to differ in many respects from other similar works. 
We would particularly direct attention to the chapter on the 
Division of Land. 

Of the Tables, we would remark, that all the type has been 
cast expressly for this work, and is made to conform with the 
old style of figures, which is admitted by all computers to 
give less fatigue to the eye than the more regular form in 
common use. To insure accuracy in these tables, they have 
been carefully compared with standard copies. 

. AT GEO. R. PERKINS. 

Albany, .November, 1851. 



CONTENTS. 



CHAPTER I. 

Page 

First Principles of Plane Trigonometry 1 

Definition of an Angle 1 

Definition of Sines, Tangents, Secants, &c 4 

To find the Sine and Cosine of the Sum and Difference of two Arcs 9 

Numerical Values of Sines, Tangents, &c. 12 

CHAPTER II. 

Explanation of Table I. of Logarithms 17 

Arithmetical Calculations by Logarithms 24 

Arithmetical Complement ,. 27 

Explanation of Table III. of Natural Sines and Tangents 28 

Explanation of Table II. of Logarithmic Sines and Tangents 29 

Explanation of Table IV., the Traverse Table 35 

CHAPTER III. 

Solution of Right Triangles 37 

Additional Examples of Right Triangles 44 

CHAPTER IV. 

Solution of Oblique Triangles 45 

Additional Examples of Oblique Triangles 55 

CHAPTER V. 

Mensuration of Surfaces 57 

CHAPTER VI. 

Mensuration of Solids 7S- 



Vlll CONTENTS. 



CHAPTER VII. 

Pago 

Land Surveying ...*. 85 

Preliminary Remarks, Description of Instruments, (fee 85 

Instruments for laying down or Plotting Surveys SS 

Instruments for measuring Angles 90 

CHAPTER VIII. 

Surveys with the Chain only ". 91 

Surveys made with the Chain and Compass 94 

Examples for Practice 105 

CHAPTER IX. 

Rectangular Method of computing Areas 109 

Rectangular Method of Plotting 116 

Examples in Rectangular Surveying 118 

CHAPTER X. 

Problems on the Division of Land 126 

CHAPTER XL 

Miscellaneous Problems useful to the Surveyor 140 



TRIGONOMETRY. 



CHAPTEK I. 



FIRST PRINCIPLES OF PLANE TRIGONOMETRY. 

§ 1 . Trigonometry is that science which investigates the re- 
lations of the sides and angles of triangles. 

When confined to plane triangles, it is called Plane Trigo- 
nometry. 

Definition of an Angle. 

§ 2. When two straight lines, ■ AB, AC, 
meet each other, the opening between these 
lines is called an angle. This angle or open- 
ing, which is read BAC or CAB, or simply 
the angle at A, does not depend upon the 
lengths of these lines, but only upon the dif- 
ference of their directions. 




§ 3. If any straight line, as 
AB, revolve about A as a cen- 
tre, in such a manner that the 
part AC shall take the succes- 
sive positions AC 1? AC 2 , AC 3 , 
&c, then will the arc described 
by the point C increase at the 
same rate as the angle increases ; 
so that the arc CqQl is to the arc 
C C 2 , as the angle C AC X is to the 

angle C AC 2 ; and the same for other arcs and their correspond- 
ing angles. Hence, the arcs thus described may be taken as 
measures of their corresponding angles. 

§ 4. When the line AC has reached the position AC 3 , so 
that the arc C C 3 is a quadrant, or one-fourth of the entire cir- 




2 TRIGONOMETRY. [CHAP. I. 

cumference, the angle C AC 3 measured by this quadrant, is 
called a right angle. The right angle is usually taken as the 
unit angle; and all angles less than a right angle are called 
acute angles, and are each measured by an arc less than one- 
fourth of an entire circumference. 

When the line AC has reached the position AC 5 , the point 
C has passed over an arc equal to one-half of the entire circum- 
ference, or over an arc which is the measure of two right angles. 
Hence, when two lines meet from opposite directions, they are 
said to form an angle equal to two right angles. 

An angle such as C AC 4 , which is greater than a right angle 
and less than two right angles, is called an obtuse angle. 

§ 5. All the foregoing relations hold good, whatever be the 
length of the radius AC . For simplicity, we shall hereafter 
use such arcs, for the measure of their corresponding angles, as 
are described with a unit radius. 

The Greek letter * is usually employed to denote the semi- 
circumference of a circle whose radius is a unit, or, which is the 
same thing, it represents the ratio of any circumference to its 

diameter. Hence is the length of an arc called a quadrant, 

which is the measure of a right angle. The numerical value of 
* is as follows : 

*=3-1415926535897932384, &c.= semi-circumference, 
when the radius=l. (See Geom. B. V. Prop. XIII.) 

§ 6. If the whole circumference be divided into 360 equal 
parts, one of those parts is called a degree. Degrees are also 
divided into 60 equal parts, called minutes / minutes are simi- 
larly divided into 60 equal parts, called seconds, and so on for 
other subdivisions. Thus 43° 14' 12" denotes an angle whose 
measuring arc consists of 43 degrees, 14 minutes, and 12 sec- 
onds. In the same way 90° denotes an angle whose measuring 
arc consists of \ of 360 degrees, and whose length is therefore 

*- = 1*5707963267948966192, &c. From the above value of <r, 

2i 

which is the arc of 180°, it is easy to find the length of an arc 
corresponding to any angle expressed in degrees, minutes, and 
seconds. Thus, we find, 



§7.] 



TRIGONOMETRY. 



E F 

T = — . Consequently, 



T .i_ of ir=l° =0-01745329251994329577, &c. 

-so of ih> of «-V =0-00029088820866572160, &c. 

eV of <fo of rio of *=1"=0-00000484813681109536, &c. 

Modern French writers, instead of using the sexagesimal di- 
vision, use the centesimal / and it is to be regretted that the 
latter is not universally used, on account of the great ease with 
which all calculations are made in that division. 

If E denote the number of English degrees in a given angle, 
and F denote the number of French grades in the same angle, 
we shall obviously have 

90 ~ 100' ~ * 9 10' 
E = T VofF = F- T V ofF; and F = -V- of E =E + £of E. 

§ 7, When the sum of two angles is equal to a right angle, 

those angles are mutually complements of each other. In such 

. it 
case, the sum of their measuring arcs is -, and the sum of the 

degrees which these arcs contain is 90°. When the sum of two 
angles is equal to two right angles, these angles are mutually 
supplement of each other : the sum of the arcs which measure 
these angles is equal to *, and 
the sum of the degrees which 
they contain is 180°. Thus the 
angles C AC„ C^ACs, are mutu- 
ally complements of each other. 
Also if we denote any arc by <z, 

its complement will be -— #, 

and its supplement will be <*— a. 
If an angle is expressed in de- 
grees, as A , where A° denotes 
the number of degrees in the arc which measures the given an- 
gle, then will 90°— A denote the number of degrees in the arc 
which measures its complement. For brevity, we say that 

if 
a and -—a are complementary arcs, and that A° and 90°— A 

are complementary degrees. For a like reason, a and *— a are 
supplementary arcs, and A° and 180°— A° are supplementary 
degrees. 




TRIGONOMETRY. 



[CHAP. I. 



Definition of Sines, Tangents, Secants, (&c. 

§ 8. In a right triangle the sine of either of the acute angles 
is the quotient obtained by divi- 
ding the side opposite the given 
angle by the hypotenuse. 

Thus, in the right triangle ABC, 
if we represent the base, perpen- 
dicular, and hypotenuse, by b, p, 
and h respectively, we shall have 

sine A = ~- sine C= T . 
h h 

The tangent of either of the acute angles is the quotient ob- 
tained by dividing the side opposite the angle by the adjacent 
side. Thus, 




P. 



tangent A = ~ ; tangent C = 



V 



The seca/nt of either of the acute angles is the quotient ob- 
tained by dividing the hypotenuse by the side adjacent the 
given angle. Thus, 

secant A = T : secant C = — . 
o p 

The cosine, cotangent, and cosecant of any angle' are respect- 
ively the sine, tangent, and secant of its complement. The two 
acute angles of a right triangle being complements of each other, 
it follows that we shall have these relations : 



sin. A = cos. C = -|- . (1) 

7 

cos. A = sin. C = -t-. (2) 

tang. A = cotan. C = ~. (3) 

7 

cotan. A = tans:. C = — . (4) 

p 

sec. A = cosec. C=—. (5) 

cosec. A = sec. C = — . (6) 

p ' 



> 



■ • (A). 



§ 9.] TRIGONOMETRY. 

From the above relations, we immediately find 
sin. A p 



sin. A 



= tang. A. (1) 

cot, A. (2) 

= -^ = sec. A. (3) 

= cosec. A. (4) 



cos 

cos. A 5 

sin. A p 

1 h 

cos. A b 

1 K 



(B). 



v 2 + o 2 
sin* A + cos. 2 A = =^P- = 1 (5) 



The exponent 2, equation (5) of (B), which is used to denote 
the square of the sine and cosine of the angle A, is placed im- 
mediately after sin. and cos., so that sin. 2 A is the same as 
(sin. A) 2 , cos. 2 A is the same as (cos. A) 2 . 
. From the above relations, we see that the sine and cosecant 
are reciprocals of each other ; cosine and secant are also recip- 
rocals ; so also are the tangent and cotangent. 

§ 9. If from one extremity of the arc which measures an an- 
gle, a perpendicular be drawn to the diameter which passes 
through the other extremity, such perpendicular will be the 
sine of that angle. Thus. CjDj is the sine of the angle CoAC^. 
For we have (§ 8) defined the sine of this angle to be the quo- 
tient obtained by dividing C^ by AC^, which quotient be- 
comes CiDi, since the divisor is the 
radius of the circle, and therefore 
(§ 5) equal to unity. In the same 
way it may be shown that C 2 D 2 is 
the sine of the angle C AC 2 , that 
C 4 D 4 is the sine of the angle C AC 4 . 
As the arc is the measure of angles, 
we say that C^, C 2 D 2 , C 4 D 4 , are 
respectively the sines of the arcs 
C C l5 C C 2 , C C 4 . 

Passing from the angle to the arc, we also say, when the arc 
exceeds the semi-circumference, that C 6 D 6 , C 8 D 8 , are respectively 
the sines of the arcs C C 5 C 6 , C C 5 C 7 C 8 . 




TRIGONOMETRY. 



[CHAP. I. 



In all these cases we suppose the arc to be estimated from 
the point C , at the extreme right of the circle, upwards and 
around towards the left. When angles are estimated from C 
downwards around towards the left, they are considered as neg- 
ative arcs. Thus, C AC 8 is considered as a negative angle, 
measured by the negative arc C C 8 . By reference to the dia- 
gram, it will be readily seen that so long as a positive arc does 
not exceed m or 180°, the sines are all situated above the hori- 
zontal diameter, and are considered as positive ; for arcs greater 
than 180° and less than 360°, their sines are situated below the 
horizontal diameter, and are considered as negative. 

§10. If from one extremity of an 
arc a tangent line be drawn, and 
limited by its intersection with the 
radius drawn through the other ex- 
tremity of the arc, then will this 
portion of the tangent line thus in- 
cluded between the radius and the 
radius produced, be the trigonomet- 
rical tangent of the arc. And the 
radius thus produced, or simply the 
produced part, will be the secant of 
the arc. Thus, CoDj is the tangent 
of the arc CqC^ and C D 3 is the tan- 
gent of the arc C C 3 , in the same way C D 5 , C D 7 are respectively 
the tangents of the arcs C C 2 C 5 , C C 2 C 4 C 7 . For, by the former 
definition (§ 8), the tangent of the angle C AD l5 which is meas- 
ured by the arc CoCj, is the quotient obtained by dividing C Dj 
by AC , which quotient becomes CoDj, since AC , the radius, is 
a unit. Also the secant of this angle is the quotient obtained 
by dividing AD X by AC , which quotient becomes AT> V When 
the arc terminates in the first and third quadrants, the tangents 
are counted on the line D^ from C upwards, and are consid- 
ered as positive. But in the second and fourth quadrants, the 
tangents are counted from C downwards, and are considered as 
negative. 

The secants of the arcs C C„ C C 3 , C C 2 C 5 , C C 2 C 4 C 7 , are re- 
spectively AD , AD 3 , AD 5 , AD 7 . By inspecting the diagram 
it will be seen that the secants represented by the dotted lines 




§".] 



TRIGONOMETRY. 



consist of the produced part of the radius, while those repre- 
sented by the full lines consist of the radius together with the 
produced part; the latter are considered as positive and the for- 
mer as negative. Hence in the first and fourth quadrants the 
secants are positive, and in the second and third quadrants they 



are negative. 



§ 1 1. These different lines may be clearly exhibited in the 
four quadrants as follows : 



First quadrant. 




Third quadrant. 




Second quadrant. 
F G 




Fourth quadrant. 




In the above diagrams the dotted lines are considered as 
negative and the full lines as positive. 

The letters in the four diagrams are so arranged that in each 
case BC counted in the positive direction (§ 9) is the arc, CD 
the sine, CH the cosine, BE the tangent, GF the cotangent, AE 
the secant, and AF the cosecant. 



8 TRIGONOMETRY. [CHAP. I. 

The algebraic sines of these lines will be as follows : 

In In In In 

1st quad. 2d quad. 3d quad. 4th quad. 

Sine and cosecant, + + — — 

Cosine and secant, + — — + 

Tangent and cotangent, -f — -f — 

§ 12. By carefully inspecting the diagrams of §11, we see 
that denoting any arc when considered as positive by #, it will, 
when counted in an opposite direction, be denoted by — a, and 
the following relations will hold good for negative arcs : 

sin. (— a)=— sin. «; cos. (•— a)=cos. a. 

tang, (—a)—— tang. a\ cotan. (—$)=— cotan. a. 

sec. (— «)=sec. a\ cosec. (— a)=— cosec. a. 



§13. If the arc KC is equal to the 
arc BC, then will the arc BC be the 
supplement (§ 7) of the arc BO. De- 
noting the arc BC by a, we have ob- 
viously the following relations : 



4 

sin. 0=sin. (180°— a) ; cos. a= — cos. (180°— a). 

tang, a—— tang. (180° — a) ; cotan. a=— cotan. (180°— a). 

sec. a= — sec. (180°— $); cosec. «=cosec. (180°— a). 

§ 1 4. The following particular values should be carefully 
noted by the student : 




0° 


90° 


180° 


270° 


360° same as 0° 


Sine . . 


+ 1 





-1 





Cosine . + 1 





-1 





+ 1 


Tangent . 


GO 





GO 





Cotangent go 





GO 





GO 


Secant . + 1 


GO 


-1 


GO 


-1 


Cosecant go 


+ 1 


00 


-1 


GO 



§15-] 



TRIGONOMETRY. 



In general, if n denote any integral number, including also 
the value of n=0, we shall have, 

: sin. 180° = sin. 2 n x 90° = 

= sin. (4^ + l)x90°=l 

:sin. (4?i-f3)x90 o = -l 

:cos. 4^x90° = 1 

= cos. 270° = cos. (2 n + 1) x 90° = 

:cos. (4^ + 2)x90° = — 1 

= tang. 180° = tang. 2^x90° = 

= tang. 270° - tang. (2 n + 1) x 90° = oo 

= cotan. 180° = cotan. 2 n x 90° = oo 

s cotan. 270° = cotan. (2 n + 1) x 90° = 

= sec. 4?ix90°=l 

: sec. 270° = sec. (2 n + 1) x 90° = oo 

:sec. (4^-f 2)x90° = -l 

; cosec. 180°= cosec. 2^x90°= oo 

: cosec. (4c n + 1) x 90° = 1 

:cosec. (4:^ + 3)x90 o = -l 



sin. 


0° 


sin. 


90° 


sin. 


270° 


COS. 


0° 


COS. 


90° 


COS. 


180° 


tang. 


0° 


tang. 


90° 


cotan. 


0° 


cotan. 


90° 


sec. 


0° 


sec. 


90° 


sec. 


180° 


cosec. 


0° 


cosec. 


90° 


cosec. 


270° 



§ 15. To find the sine and cosine of the sum and difference 

of two arcs. 

• 
Let the angle ~BAC=a ; that is, let D 

a denote the length of the arc which 
measures this angle ; also let the an- 
gle CAD be denoted by o ; then will 
BAD be denoted by a-\-o. 

Draw EF perpendicular to AC, and 
from the points E and F draw EG 
and FH perpendicular to AB ; also 
draw FK perpendicular to EG. Since the sides of the triangle 
EFK are respectively perpendicular to the sides of the triangle 
xiFH, these triangles are similar. (Geom. B. IV. Prop. XII.) 
Hence, the angle FEK is equal to FAH, equal to a. 

. , y x . EG HF + KE HF , KE 
sm. (0+5) = — =: 




AE 



AE ' AE 



HF AF KE EF 

AF X AE + EF X AE* 



10 



TRIGONOMETRY. 



[CHAP. I. 



HF AF KE 

By our definitions (§ 8), -^— r = sin. a ; -r-g = cos. b ; ^ 



cos. a ; 



EF 



AE 



sin. b. Hence, we have 



sin. {a-\-b)~ sin. a cos. b + cos. & sin. &. 
Again, we have 



, .. , xx AG AH-KF AH 



KF 



AE 



AE 



AE AE 



AH AF KF EF x ...-..' . , 

-—rr X -r-^r — -^rn X -ttt = cos. a COS. o — sin. « sm. 0. 
AF AE EF AE 

For the sine and cosine of a— 5, let the angle BAC = #, and 
the angle CAD = b ; then will BAD = a—b. 

Then, as in the former diagram, c 

we have the triangle EFK similar 
to the triangle AFH, and the angle 
KFE equal to the angle FAH, equal 
to a. 




. , , s EG HF-KF HF AF 
sin. {a—b) = -jr^ = rT? — = - rT? x 



KF FE 
X AE 



cos. («-&)=_ 



AE AE AF AE FE 

sin. a cos. b— cos. a sin. b. 



AG AH + KE AH AF , KE FE 



= ^T X 



AE AF AE ' FE 

cos. a cos. b -f sin. a sin. b. 

Collecting these results, we have 

sin. {a + b) = sin. a cos. 5 -1- cos. a sin. 5. . . 

sin. (a—b)= sin. a cos. 5 — cos. a sin. 5. . . 

cos. (a + b) = cos. $ cos. b — sin. & sin. b. . . 

cos. (a—b) = cos. # cos. & + sin. a sin. 5. . . 

If we make b == <z, equations (1) and (3) will give 

sin. 2 a = 2 sin. & cos. a, . 
cos. 2 # = cos. 2 (X— sin. 2 a. 

From (5) of (B), § 8, we have 

l=sin. 2 #4- cos. 2 a 



*AE~ 



(2.) 
(3.) 



(5.) 
(6.) 



(TO 



§ 16.] TRIGONOMETRY. 11 

The sum and difference of (6) and (7) give 

1 + cos. 2 a = 2 cos. 2 a, (8.) 

1 — cos. 2 a = 2 sin. 2 a. (9.) 



Hence, sin. a — \ ^2 — 2 cos. 2 a, . . (10.) 



cos. a = J ^2 + 2 cos. 2a> . . (11.) 

Equations (5) and (6) make known the sine and cosine of a 
double arc in terms of the sine and cosine of the arc itself. 
Equations (10) and (11) give, conversely, the sine and cosine of 
half an arc in terms of the cosine of the arc itself. 

Dividing (1) by (3), we have 

sin. (a + b) _ sin. a cos. b + cos. a sin. b 
cos. {a + b) cos. a cos. b — sin. a sin. V 

Dividing numerator and denominator of the right-hand mem- 
ber each by cos. a cos. b, we have 

sin. & sin. b 
sin. (a + b) cos. a cos. b 



cos. (a + b) 1 sin. <z sin: J ' 
cos. & cos. b 

which becomes (§ 8), 

, . 7N tang. & -f tang, b ,_,-. 

tang. (a+b)= - — f ' 6 , . . . (12.) 

° 1 — tang, a tang, b ' 

§ 16. Equations (1), (2), (3), and (4) (§ 15), give as follows : 

sin. (a + J) + sin. (a—b) = 2 sin. « cos. 5. (1.) 

sin. {a + 5) — - sin. {a—b) = 2 cps. a sin. 5. (2.) 

cos. (a— b) + cos. (# + J) = 2 cos. a cos. 5. (3.) 

cos. (a — b) — cos. (a + J) = 2 sin. # sin. b. (4.) 

If in these results we substitute p for a + J, and <? for #—&, 
which gives a = £ (#> + #) and b = h (p—o), they will become 

sin.^> + sin. q = 2 sin. h (p + o) cos. -J (p—q)- (5.) 
sin. j? — sin. ^ = 2 cos. J (^> +g) sin. i (p — q)- (6.) 
cos. ^ + cos. jt> = 2 cos. J (^ + a) cos. -J (p—q)- (7.) 
cos. # — cos. p = 2 sin. J (p -{-q) sin. ^ (p—q)- (8.) 



12 TRIGONOMETRY. [CHAP. I. 

Dividing (5) by (6), we have 

sin. j!? + sin. q _sin. J (p-\-q) cos. \ (p — q) 
sin. p — sin. q cos. \ (p ~\-q) sin. J (p — qf 

hence, 

sin.^) + sin. ^ _sin. \ (p + q) ^sin. i (p—q) _tang. i(p-\-q) 
sin.^?— sin. q cos. i{p+q) ' cos. ± (p—q) tang. \ (p — q)' 

(9.) 

Numerical Values of Sines, Tangents, <&c. 

§ 17. Having deduced a few of the most simple relations of 
the trigonometrical functions of angles, we will now proceed to 
determine their numerical values. 

Sines of very small angles are obviously very nearly equal 
to the arcs which measure these angles. We have found (§ 6) 
that the length of an arc of V is equal to 0*0002908882, &c. If 
we regard this as the sine of 1', from which, as will be hereafter 
shown, it does not differ even in its eleventh decimal figure, we 
may find the cosine of V as follows (§ 8) : 



cos . l'^Vl-sin. 2 l'=0-99999995rr, &c. 

Having thus found the sine and cosine of 1', we may continue 
our work for larger angles by the aid of equations (1) and (3), 
(§16), which give give 

sin. (a + b) = 2 sin. a cos. b— sin. (a~b). 
cos. (a + b) — 2 cos. a cos. h— cos. (a—b). 

Putting b=V and a—\\ 2', 3', 4', &c, successively, we shall 
obtain 

sin. 2' =2 sin. 1' cos. V — sin. 0'. 
sin. 3' =2-sin. 2' cos. 1'— sin. 1'. 
sin. 4' = 2 sin. 3' cos. 1'— sin. 2'. 
sin. 5' =2 sin. 4' cos. 1' — sin. 3'. 
&c. &c. &c. 

cos. 2' = 2 cos. 1' cos. 1'— cos. 0'. 
cos. 3' = 2 cos. 2' cos. V — cos. 1'. 
cos. 4' = 2 cos. 3' cos. V — cos. 2'. 
cos. 5' = 2 cos. 4' cos. 1'— cos. 3'. 
&c. &c. &c. 



18.] 



TRIGONOMETRY. 



13 



Using the above value of sine and cosine of 1', executing the 
work above indicated, and preserving only nine decimal places, 
we find 



sin. l'=O000290888. 
sin. 2 , =0-000581Y76. 
sin. 3'=O000872665. 
sin. 4'=0-001163553. 
sin. 5'=0-0014:5444:l. 
&c. &c. 



cos. l'=0-999999958. 
cos. 2'=0-999999831. 
cos. 3 / =0-999999619. 
cos. 4'=0999999323. 
cos. 5'=0'999998942. 
&c. &c. 



The work might be continued in this way to any desired 

extent. 




§ 18. We will now seek formulas 
which shall give the sine and cosine 
of any arc without our being obliged 
first to compute those of a smaller 
arc. 

Denote the arc BC, which meas- 
ures the angle BAC, by x, the radius 
being unity. 

Then assume, 



CD = sin. x = a + a x x + <h ®* + a z $ + a i ^ + <% $ +, &c. (1.) 
DA =cos. x — b + b x x + b 2 x 2 + b 3 x* + b 4 x* + b 5 x 5 +, &c. (2.) 

When x = 0, the sine of x becomes zero, which requires a to 
= 0. Since the sine of a negative arc (§ 12) is the same as mi- 
nus the sine of the same arc taken positively, it follows that the 
expression (1) for the sine of x must be of such a form as to 
change the algebraic signs of all its terms when —a? is written 
for + #, consequently it cannot contain any even powers of x. 
Therefore a 2 = ; a A = 0, &c. 

Again, when x = 0, the cosine of x becomes 1, so that b = l. 
And, since the cosine of a negative arc is precisely the same as 
the cosine of the same arc taken positively, it follows that the 
expression for the cosine of x must be of such a form as not to 
change the algebraic signs of any of its terms when — x is writ- 
ten for + #, consequently it cannot contain any odd powers of x. 
Therefore b x = ; b 3 = ; b 5 = 0, &c. 



14 TRIGONOMETRY. [CHAP. I. 

Equations (1) and (2) must therefore assume the following 
forms : 

sin. x — di x + #3 a^ + % $ + <h $ +, &c. . . (3.) 

COS. X — 1 + & 2 X 2 + ^4 # 4 + K $ +, &C. . . . (4.) 

If we suppose the arc x to be exceedingly small, we may 
obtain a very close approximate value for the sine of a?, in (3) ; 
by retaining only the first power of a?, we thus find 

sin. » = «!», very nearly. 

But in very small arcs the sine and the arc are very nearly 
equal ; hence, when x is very small, we must have sin. x = a?, 
very nearly. Consequently a y = 1. 

Using this value of # l5 equations (3) and (4) become 

sin. x = x + a 3 a? 3 + a 5 x> + « 7 x 1 +, &c. . . (5.) 
cos. x = 1 + 1 % x 2 + h x* + & 6 a? 6 -f, &c. . . (6.) 

It now remains to find the other coefficients, # 3 , <%, #7, &c, 
6 2 , £4, &6i & c « For this purpose we proceed as follows : 
In (5) write 2 x fo»a?, and we obtain 

sin. 2 a = 2 & + 8 a 3 a? 8 + 32 a 5 a> 5 + 128 <% x 1 +, &c. (7.) 
Dividing (7) by 2, we have 

% sin. 2 a? = x + 4 <2 3 a? 3 + 16 a b x 5 + 64 <z 7 a? 7 +, &c. (8.) 
Taking the product of (5) and (6), we find 



sin. x cos. x = x-\-a 3 \ 3 + a b \ + a? 



+ h 4 ) + h 4 a 3 

+ b 6 J 



^ 7 +, &c. (9.) 



The left-hand members of (8) and (9) being equal [§ 15, 
eq. (5)], their right-hand members must also be equal ; hence 
equating the coefficients of like powers of a?, we obtain 

4 a 3 = a + 5 2 

16 a b - % + 5 2 % + h } • • (!0.) 

64 7 = 7 + b 2 a b + 6 4 a z -f 6 tf 
&c. &c. 



§ 18.] TRIGONOMETRY. 15 

Equations (5) and (6), when squared, become respectively 
Bin.»3=rf + 2fl,*»+ «."U+ &c . m ; (1L) 

+ 2<% ) 

co8."a = l'+2 6,rf + V)^ + 26 6 \tf+^.\l%) 

+ 25 4 i +2 5 2 5j ' v } 

If from the sum of (11) and (12) we subtract 1, we shall obtain 



sin. 2 x + cos. 2 a?— 1=+ 1 



x 1 



+2 a B ) +% 



la* 4 - 



+ 2* 2 f -+^ Vrf+2* • +&ca3) 

+2&J +2& 6 h^+> &c -(l*0 

+2 & 2 &4. 

Since the left-hand member of (13) is equal to zero [§ 8, eq. 5 
of B], the right-hand member must also equal zero ; hence the 
coefficients of the different powers of x must equal zero, which 
leads to the following conditions : 

1+2Z> 2 = ) 

2a 3 + b 2 * + 2bt=0 J. . . (14.) 

&c. &c. 

Equations (10) and (14) give immediately these results : 

b, = -i = 



< h— — 6 ~~ 



1x2* 

1 



j — 

24 



lx2x 3 
1 



120 



cu = 



1x2x3x4' 
1_ 

1x2x3x4x5* 
1 



fa 72 ° 1x2x3x4x5x6* 



#7 — 5040 : 



1x2x3x4x5x6x7' 
&c. &a. &c. 

Hence, equations (5) and (6) become 

syr$ /y*> ry** 

IAS - . ' W dU 



Bin. x = x- 



cos.a? = l 



+ 



1x2x3 1x2x3x4x5 1x2x3x4x5x6x7 



x 2 



+ 



x 4 



a? 6 



-, &c. 
(15.) 



1x2 1x2x3x4 1x2x3x4x5x6 



■.+, &c. (16.) 



16 



TRIGONOMETRY. 



[CHAP. I. 



If we divide the right-hand member of (15) by the right-hand 
member of (16), we shall obtain an infinite series, giving the 
value of tang. a?, as follows : 



of 



, 2^ , 17 a? 
tan g .x=x + J + — +— - 



&c. 



Other series might be found by combining (15) and (16) for 
the cotan. a?, sec. a?, and cosec. x. 

The arc of 1' has already been found [§ 6] to be equal to 
0-0002908882086, &c. Putting this value for x, in the above 
series, we find 



x 6 



1 x2 

*3 



Of 



= 0-0000000423079, 
0-0000000000041. 



1x2x3 
If we confine ourselves to thirteen decimals, we shall obtain 



sin. l'=x- 



Qf 



1x2x3 



= 0-0002908882045 ; 



COS. l'= 1 



X* 



1x2 



0-9999999576921. 



From this we see that the sine of 1' does not differ from its 
corresponding arc until after we pass the 11th decimal place, 
as was asserted under § 17. 

For ordinary purposes, seven decimal places is as accurate 
as is desired. Having already (§ 17) computed the sine and 
cosine of each minute as far as 5', we will now, by the aid of 
equations (15) and (16), continue the computation, limiting 
ourselves to seven decimals, and shall obtain as follows : 



7' = 

8' = 
9' = 
10' = 
11' = 
12' = 
13' = 
14' = 
15' = 



•0017453, sin. = 0'00l7453, cos. = 0*9999985 


0020362, 


' =0-0020362, 


' = 0-9999979 


0023271, 


' = 0-0023271, « 


' =0-9999973 


0026180, 


< =0-0026180, 


« = 0-9999966 


0029089, 


< = 0-0029089, 


< = 0-9999958 


0031998, 


' = 0-0031998, 


1 =0-9999949 


0034907, 


' = 0-0034907, 


' = 0-9999939 


0037815,. < 


' = 0-0037815, 


« = 0-9999928 


0040724, 


' = 0-0040724, 


< =0-9999917 


0043633, 


' = 0-0043633, < 


« = 0-9999905. 



19.] 



arc of l o = 0'0l74533, 
2° = 0-0349066, 
3° = 0-0523599, 
4° = 0-0698132, 
5° = 0-0872665, 
6° = 0-1047198, 
7° = 0-1221730, 

" 8° =0-1396263, 
9° = 0-1570796, 

" 10° == 0-1745329, 



TRIGONOMETRY. 






legrees, we find 






sin. = 0-0174524, 


COS. 


= 0-9998477. 


" =0-0348995, 


it 


= 0-9993908. 


" = 0-0523360, 


tt 


= 0-9986295. 


" =0-0697565, 


a 


= 0-9975641. 


" =0-0871557, 


a 


= 0-9961947. 


<' =0-1045285, 


tt 


= 0-9945219. 


" = 0-1218693, 


it 


= 0-9925462. 


" =0-1391731, 


a 


= 0-9902681. 


" = 0-1564345, 


a 


= 0-9876883. 


" =0-1736482, 


tt 


= 0-9848078. 



17 



Having in this way computed the sines and cosines, we may 
[see equations (B), § 8] obtain the tangents by dividing the 
sines by their corresponding cosines ; the cotangents will be 
obtained by dividing the cosines by the sines. The reciprocal 
of the cosines will give "the secants, and the reciprocal of the 
sines will give the cosecants. 

The values of the sines, cosines, tangents, and cotangents are 
given in Table III. 



CHAPTEE II. 



EXPLANATION OF TABLES. 



TABLE T. 



LOGARITHMS. 



§ 19. This table gives the logarithms of all numbers from 1 
to 10000. 

For the method of calculating these logarithms, the student 
is referred to my " Treatise on Algebra," chap. IX. 

The common logarithm, or Briggean logarithm, as sometimes 
called, in honor of the inventor Briggs, has 10 for its base. 
Hence, for common logarithms, we have 

2 



18 



TRIGONOMETRY. 




[a 


, that is, is the logarithm of 1 


cc cc -1 cc cc 


cc 


" 10 


cc cc o cc cc 


cc 


" 100 


cc cc g cc cc 


cc 


" 1000 


cc cc ^ cc a 


cc 


" 10000 


1, " " 5 " " 


cc 


"100000 


&C. 




&c. 



[chap. II. 



10»=1 

10 x =10 
10 2 =100 
10 3 =1000 
10 4 = 10000 
10 5 =100000, 
&c. 

If we use negative exponents, we shall have 

10~ 1 =0 , 1 , that is, —1 is the logarithm of 0*1 
10~ 2 =0-01 , u " -2 " " " " 0-01 

10" 3 =0-001 , " " -3 " " " " 0-001 

10- 4 =0-0001 , " " -4 " " " " 0-0001 

io~ 5 =o-ooooi, " " -5 " " " " 0-00001 
&c. &c. 



From the above, we see that the logarithm of any number 
between 1 and 10 is a proper fraction between and 1. The 
logarithm of any number between 10 and 100 is 1 plus a proper 
fraction. The logarithm of any number between 100 and 1000 
is 2 plus a fraction. 

We also see that the logarithm of any number between 1 and 
0*1 is some number between and — 1 ; it may therefore be 
represented by — 1 plus a fraction. For a similar reason, the 
logarithm of any number between 0'1 and - 01 may be repre- 
sented by —2 plus a fraction. The logarithm of any number 
between 0'01 and 0*001 is —3 plus a fraction. 

Hence, we see that logarithms of all numbers greater than 10 
or less than 1 consist of an integral part, positive or negative, 
plus a proper fraction. The integral part is called the charac- 
teristic^ and may readily be assigned by the following 



RULE. 

The characteristic of the logarithm of any number greater 
than 1 is one less than the number of places of figures which 
express the integral part of the given number. 

The characteristic of the logarithm of a decimal fraction is 
a negative number, and is equal to the number of places by 
which the first significant figure is removed from the units'* place. 



21.] 



J 


TRIGONOMETRY. 


ms, we have as follows : 




Number. Characteristic. 


Number. 


4 





0-4 


48 


1 


0-46 


138 


2 


0-375 


2304 


3 


0-05 


4-7 





0-0578 


37-04 . 


1 


0-006 


120-005 . 


2 


0-00675 


2178-88 . 


3 


0-00035 



19 



Characteristic. 
-1 
-1 
-1 

-2 
-2 
-3 
-3 
-4 



The characteristic being so readily obtained by means of the 
above rule, has been omitted in the tables, except in the small 
table on page 1, where are found the logarithms of all numbers 
from 1 to 100, with their characteristics. But for all the other 
numbers of our table only the decimal part of the logarithms 



are given. 



The decimal part of all logarithms are regarded as positive. 
The characteristic may, however, be considered as negative. 
When this is the case, it is usual to place the negative sign im- 
mediately over the characteristic. Thus the logarithm of 0*75 is 
1-875061, or 0-875061-1. 

§ 20o To find, in the table, the logarithm of any number 
from 1 to 100. 

Seek for the given number in one of the columns headed N, 
of the first page of the tables of logarithms, and against it on 
the right in the next column, 
We thus find 



will be found the logarithm. 



log. 7 = 0-845098, 
log. 39 = 1-591065. 



§21. To find the logarithm of any number consisting of 
three places of figures. 

Seek the given number in one of the left-hand columns headed 
]ST, and against it in the column headed will be found the de- 
cimal part of the logarithm, observing that if only four figures 



20 TRIGONOMETRY. [CHAP. II. 

are given in column 0, they are the last four : the first two are 
to be taken from the number directly above which contains six 
places of figures. Thus, we find 

log. 617 = 2-790285, 
log. 635 = 2-802774. 



§ 22. To find the logarithm of a number consisting of four 
places of figures. 

Seek the first three figures in column headed !N", then passing 
horizontally across the page until you reach the column headed 
with the fourth figure of the given number, and you will have 
the last four decimal figures of the logarithm. The first two 
figures are to be taken from the column headed ; observing, 
if the four figures found, stand opposite to a row of six figures 
in the column 0, to use the first two. But if the four figures 
found are opposite a line of only four figures, you are then to 
ascend the column till you come to a line of six figures, and 
then to use the two left-hand figures. The six figures thus ob- 
tained will be the decimal part of the logarithm. The charac- 
teristic is to be found by the Rule under § 19. Thus, we find 

log. 3657 = 3-563125, 
log. 7641 = 3-883150. 

In some portions of the table, in the columns headed 1, 2, 3, 4, 
&c, the character ♦ is to be found in place of a figure, which in- 
dicates that the two figures of the first column, which are to be 
prefixed, have changed, and are to be taken from the horizontal 
line directly below. This change of the two left-hand figures of 
the logarithm is indicated by an asterisk placed in the column 
0. The place occupied by this character is to be supplied with 
a zero. The two figures from the column must also be taken 
from the line below the asterisk, if the character ♦ has been 
passed over while crossing the page horizontally. Thus, we find 

log. 2138 = 3-330008, 
log. 2298 == 3-361350, 
log. 3237 = 3-510143. 



§ 23.] TRIGONOMETRY. 21 

§ 23. To find the logarithm of a number consisting of fime 
or more places of figures. 

For example, let us seek the logarithm of 734582. We read- 
ily find as follows : 

log. 734500 = 5-865992 
log. 734600 = 5-866051 



Diff. of numb. =100 Diff. of loffs.=59 



&■ 



The difference between the first number 734500 and the given 
number is 734582—734500 = 82. Hence, if we suppose the 
difference of logarithms to be to each other as the difference of 
their corresponding numbers, which supposition is very nearly 
correct, we shall have 



-I 



100 : 82 : : 59 : 48-38, 

for the difference between the logarithm of 734500 and the log- 
arithm of 734582. Hence, we have 

log. 734500 = 5-865992 

+ 48-38 



log. 734582 = 5-866040 



'to 



Had there been only five figures in the given number, that 
is, only one beyond the fourth place, the first term of the above 
proportion would have been 10 instead of 100 ; had there been 
three additional figures beyond the fourth place, the first term 
would have been 1000. 

The difference between the logarithms of consecutive num- 
bers of four places of figures is given in the table in a column 
headed D. Thus by turning to the table, we find 59, our third 
term of the above proportion, immediately opposite the loga- 
rithm of 7345. 

From what has been done, we see that we may find the loga- 
rithm of a number consisting of more than four places of figures 
by the following method : 

Consider all the figures after the fourth as zeros. Then find 
the decimal part of the logarithm of the number given by the 
first four figures, observing to give a characteristic for the whole 
number of figures by rule under § 19. Take from the column 



22 TKIGONOMETKY. [CHAP. II. 

D the number which is found directly opposite the logarithm 
already taken out, and multiply it by the figures which were 
regarded as zeros, pointing off in the product as though these 
figures were all decimals ; add the result thus obtained to the 
logarithm already found, and it will give the logarithm of the 
given number. 
In this way we find 

log. 365365 = 5-562727. 
log. 635536 = 5-803140. 
log. 704307 = 5-847762. 

Note. — Since the foregoing process of finding the logarithm of a number of more 
than four places of figures is founded on the supposition that the differences of 
logarithms of different numbers are to each other as the differences of the numbers, 
which supposition is not strictly true, it follows that this method can be used only 
to a limited extent. It ought never to be employed for a number consisting of 
more than six places of figures. 

§24. To find the logarithm of a Vulgar Fraction. 

Since a vulgar fraction is the quotient of the numerator di- 
vided by the denominator, we may obtain its logarithm by sub- 
tracting the logarithm of the denominator from the logarithm 
of the numerator. Thus, the logarithm of %\ is log. 37— log. 
53 = 1-568202-1-724276 =1-843926. 

In a similar manner we find 

log. s«5 =1-960233. 
log. IJI = 1-908450. 

§25. To final the logarithm of a Decimal Fraction. 

Since we have, by the property of logarithms, 

log. 4-5 =log. f-f =log. 45— log. 10= log. 45—1; 
log. 3-65 =log. \%% =log. 365-log. 100= log. 365-2; 
log. 3-754 = log. f Jf % =log. 3754-log. 1000 =log. 3754-3 ; 

it follows that the decimal part of the logarithm of a decimal 
fraction is the same as though the number was wholly integral, 
the only difference between the logarithm of a decimal number 
and of the number considered as integral is in the character- 
istic. Hence, take out the logarithm as though the number were 
integral, and fix a characteristic according to rule under § 19. 



26.] 


TRIGONOMETRY. 


We thus find, 








log. 476 


= 2-677607 




log. 47-6 


= 1-677607 




log. 4-76 


= 0-677607 




log. 0-476 


= 1-677607 




log. 0-0476 


= 2-677607 



23 



log. 0-00476 = 3-677607 

§ 26. To find the natural number corresponding to any log- 
arithm. 

Seek in the table, in the column 0, for the first two figures of 
the decimal part of the logarithm ; the other four figures are to 
be sought for in the same column, or in any one of the columns 
1, 2, 3, &c. If the decimal part of the logarithm is exactly 
found, then will the first three figures of the corresponding- 
number be found in the column N, and the fourth figure will 
be found at the top of the page. This number must be made 
to correspond with the given characteristic of the given loga- 
rithm by annexing ciphers, or by pointing off decimals. Thus the 

logarithm 5*311754 gives 205000, 
" 4-341237 " 21940, 
" 3-759970 " 5754, 
" 2-759970 " 575-4, 
" 1-750970 " 57-54. 

When the decimal part of the logarithm cannot be accurately 
found in the table, take out the four figures corresponding to 
the next less logarithm. Then for the additional figures, sub- 
tract this less logarithm from the given logarithm, and divide 
the remainder, with naughts annexed, by the corresponding 
number taken from column D. For example, let us seek the 
number whose logarithm is 1-234567. We find the next less 
number to the decimal 0-234567 to be 0*234517, which corre- 
sponds to 1716. We also find the number in column D to be 
253. Hence 

•0-234567 t 
0*234517 



50 ; and 50 -r- 253 = 0*198, nearly. 
So that the number answering: to the logarithm 1*234567 is 



17*16198, nearlv. 



24 TRIGONOMETRY. [CHAP. n. 

ARITHMETICAL CALCULATIONS BY LOGARITHMS. 

§ 27. Multiplication by Logarithms. 

Since the logarithm of the product of two or more factors is 
equal to the sum of their logarithms, we deduce, for multiplica- 
tion by logarithms, this 

RULE. 

Add the logarithms of the factors, and the sum will be the 
logarithm of the product. 

1. What is the product of 3'65 by 56'3 ? 

log. 3-65 = 0-562293 
log. 56-3 = 1-750508 

log. of product = 2-312801, 
which gives 205-495 for the product. 

2. What is the product of 7*8 by 35-3 % Ans. 275*34 

3. What is the product of 2-13 by 0-57 ? Ans. 1-2141. 

Note. — When any of the characteristics of the logarithms are negative, we must 
observe the algebraic rule for their addition. 

4. What is the continued product of 53*7, 0-12, and 0-004 ? 

log. 5-37 =1-729974 
log. 0-12 =1-079181 
log. 0-004 = 3-602060 

product=0-025776, whose log. =2-411215 

5. What is the square of 3*7 ; that is, what is the product of 
3-7 by 3-7? Ans. 13*69. 

6. What is the cube of 3'8 ; that is, what is the continued 
product of 3-8, 3-8, and 3-8 ? Ans. 54-872. 

§ 28. For Division by Logarithms, we obviously have this 

RULE. 

Subtract the logarithm of the divisor from the logarithm of 
the dividend. 



§ 29.] TRIGONOMETRY. 25 

EXAMPLES. 

1. What is the quotient of 365 by 7*3 ? 

log. 365 = 2-562293 
log. 7-3 = 0-863323 



quotient is 5, its log. = 1-698970 

2. What is the quotient of 2-456 by 147 ? 

Ans. 1-67075, nearly. 

3. What is the quotient of 7'4 by 12-58 % Ans. 0*588235. 

Note. — "When either or both of the characteristics of the logarithms are negative, 
we must observe the algebraic rule for the subtraction of the one from the other. 

4. What is the quotient of 0-378 divided by 0-45? 

log. 0-378 =1-577492 
log. 0-45 =1-653213 



quotient = 0*84, whose log. = 1-924279 

5. What is the quotient of 0-10071 by 0-00373 % 

log. 0-10071 = 1-003072 
lop:. 0-00373=3-571709 



quotient =27, whose log. = 1*431363, nearly. 

§ 29. Involution by Logarithms. 

Since the exponent denoting any power of any number ex- 
presses how many times this number is used as a factor to pro- 
duce the given power, it follows that the logarithm of any power 
is equal to the logarithm of the number repeated as many times 
as there are units in the exponent. Hence we have this 

RULE. 

Multiply the logarithm of the number by the exponent deno- 
ting the power. 

EXAMPLES. 

1. What is the 5th power of 1-234 ? 

log. 1-234 = 0-091315 

5 multiply. 

root = 2-86137, whose log. = 0-456575 



26 TRIGONOMETRY. [CHAP. II. 

2. What is the 7th power of 05 % 



log. 0-5 = 1-698970 



7 multiply. 



root = 0-0078125, whose log. = 3*892790 

Note. — It must be kept in mind that the decimal part of every logarithm is pos- 
itive, so that, as in the last example, whatever is to carry to the product of the 
characteristic by the exponent is positive. 

3. What is the 30th power of 1-07 % Ans. 7*6123, nearly. 

4. What is the 11th power of 0*11 ? 

Ans. 0-0000000000285313. 

§ 30, Evolution by Logarithms. 

Since the exponent denoting a root indicates that the number 
is to be separated into as many equal factors as there are units 
in the exponents, we obviously have this 

RULE. 

Divide the logarithm of the number by the number denoting 
the root. 

EXAMPLES. 

1. What is the 11th root of 11 ? 

log. 11 = 1-04:1393, which divided by 11 gives 0*094672 
for the log. of the root. Hence the root = 1-24357, 
nearly. 

Note. — When the characteristic is negative, and not divisible by the exponent, 
we must put with it a sufficiently large negative integer to make it divisible, and 
then connect with the decimal portion of the logarithm an equally large positive 
number. This will be best illustrated by the following example. 

2. What is the 5th root of 0*00567 ? 

log. 0-00567 = 3-753583 = 5 + 2-753583, which divided 
by 5 gives 1-550716 for the logarithm of the root. 
Hence the root = 0*3554, nearly. 

3. What is the 3d root of 0*365 ? Ans. 0*714657, nearly. 

4. What is the 7th root of 7? Ans. 1*32047, nearly. 

5. What is the 5th root of 0*5 ? Ans. 0-87055, nearly. 



§ 32..] TRIGONOMETRY. 27 

§31. Proportion by Logarithms. 

Since the fourth term of a proportion is found by dividing 
the product of the second and third terms by the first, we ob- 
viously have this 

RULE. 

From the sum of the logarithms of the second and third 
terms, subtract the logarithm of the first term. 

"What is the fourth term of a proportion of which the first, 
second, and third terms are respectively 0-0146, 4*5, and 1*07? 

log. 4-5 =0-653213 
log. 1-07 = 0-029384 

0-682597 
subtract log. 0-0146 = 2464353 

log. of fourth term = 2-518244 
Consequently the fourth term = 329*794, nearly. 

ARITHMETICAL COMPLEMENT. 

§ 32. The subtraction of a logarithm from the sum of two or 
more logarithms is usually made to depend upon addition, by 
making use of its Arithmetical Complement, which is the differ- 
ence between 10 and the given logarithm, and is readily taken 
from the table, by beginning at the left hand and subtracting 
each figure from 9, except the last significant figure on the right, 
which must be taken from 10. Wow it is obvious, that if in- 
stead of subtracting a given number from another, we first sub- 
tract the number from 10, and then add the result, we shall, 
after rejecting 10, obtain the true difference. Hence to work a 
proportion by logarithms, we may use this second 

RULE. 

Take the arithmetical complement of the logarithm of the 
first term, and the logarithms of the second and third terms, 
and from the sum of the three reject 10 from the characteristic. 



28 TRIGONOMETRY. [CHAP. H. 

EXAMPLES. 

1. What is the fourth term of the proportion 6*5 : 30*5 : : 1*25? 

Arith. comp. log. 6-5 = 9-187087 
log. 30-5 =1484300 
log. 1-25 = 0-096910 

sum, after rejecting 10, = 0*768297, which 
is the log. of 5-86539, the fourth term. 

2. What is the fourth term in the proportion 3456 : 10*5 : : 
6543? 

ar. co. log. 3456 = 6-461426 
log. 10-5 = 1-021189 
log. 6543 = 3-815777 



fourth term = 19-8788, log. = 1-298392 

3. In the proportion 1-23 : 2-34 : : 3'45, what is the fourth 
term ? Ans. 6*56342, nearly. 



TABLE III. 

NATURAL SINES AND TANGENTS. 

§33. It is necessary to explain the arrangement of this 
table before explaining that of Table II., since the values of the 
latter have been obtained from those of the former. Table II., 
being logarithmic values, is with propriety placed immediately- 
after the table of logarithms. 

Table III. contains the natural sines and tangents to every 
minute of the first quadrant, and consequently those of the co- 
sines and cotangents. The first 9 pages are devoted to sines 
and cosines, the remainder of this table gives the tangents and 
cotangents. 

When the number of degrees does not exceed 45, they are to 
be found at the top of the page, and the additional minutes are 
given in the first or left-hand column , of the page. But if the 
degrees exceed 45, they are to be found at the bottom of the 
page, and the additional minutes are then given in the last, or 
right-hand column of the page. 



§34.] 



TRIGONOMETRY. 



29 



It will be seen by examining this table that the number of 
degrees at the top of any page added to the number at the bot- 
tom of the same, gives 89, to which adding the 60 intermediate 
minutes makes just 90 degrees. Thus, on page 70 we have 
34° at the top and 55° at the bottom, the sum of which is 89°. 

Since the cosine and cotangent (§ 8) of an angle is the same 
as the sine and tangent respectively of its complement, it fol- 
lows that by this arrangement of the table those columns which 
are marked sine and tangent at the top of the page will be 
marked cosine and cotangent respectively, at the bottom of the 
page. 

As the sine and cosine of any angle cannot exceed the radius, 
which is a unit, it follows that their values are always expressed 
in this table by a decimal. The tangent and cotangent may in 
some cases exceed a imit, and will then be expressed by a deci- 
mal joined to an integral part. 

Thus, turning to this table, we find 



sin. 17° 13'=0-29599 
tang. 17° 13' = 0"30987 
sin. 55° 43'=0'82626 
tang. 55 43'=l-4:6686 



cos. 17° 13'=0-95519. 
cotan. 17° 13'=3-22715. 
cos. 55° 43'=0'56329. 
cotan. 55° 43'=0-68173. 



TABLE II. 



LOGARITHMIC SINES AND TANGENTS. 



§ 34, This table is constructed by taking. the logarithms of 
the values given in Table III., and increasing each logarithm 
by 10. The arrangement is the same as given in the Table of 
Natural Sines, Tangents, &c. ; that is, the degrees are to be 
found at the top of the page and minutes in the first column, 
when the angle is less than 45°. When the angle is greater 
than 45°, the degrees are to be found at the bottom of the 
page and the minutes in the last column. As in the last table, 
the column marked sine at top is cosine at the bottom ; the col- 
umn marked tangent at the top is cotangent at the bottom, and 
conversely. 

Obtuse angles are also provided for in this table : when found 
at the top of the page they are at the right-hand side, and the 



30 TEIGONOMETKY. [CHAP. n. 

minutes are then to be found in the right-hand column. But 
when found at the bottom of the page they are at the left-hand 
side, and the minutes are then to be found in the left-hand 
column. 

As most cases of Trigonometry are solved by the assist- 
ance of proportions, which are most readily wrought by the 
help of logarithms, it has been found convenient to prepare 
beforehand the logarithms of the sines and tangents of all an- 
gles expressed by degrees and minutes within the limit of the 
first quadrant. 

Since the sines, as well as tangents, of many arcs are less 
than a unit, the characteristic of their logarithms will be nega- 
tive. By adding 10 to each logarithm, the characteristics will 
all be positive, and we shall not be as liable to commit errors 
in using them, as we should if some had positive characteris- 
tics, and others negative characteristics. 

§ 35. To find, in the table, the logarithmic sine, cosine, tan- 
gent, or cotangent of any given angle. 

If the angle is less than 45°, we seek the degrees at the top 
of the page and the minutes in the first column on the left ; then 
passing across the page horizontally until we come to the column 
having the appropriate heading of sine, cosine, tangent, or co- 
tangent, as the case may require, we shall find the logarithm 
sought. Thus, on page 53, we find 

sin. 35° 53' =9-767999 ; cos. 35° 53'= 9-908599. 
tang. 35° 53'=9-859400 ; cotan. 35° 53'=10'140600. 

If the angle is greater than 45°, we seek for the degrees at 
the bottom of the page, and the minutes on the right-hand side 
of the page ; then, as before, passing horizontally across the page 
till we reach the column having at the bottom the appropriate 
designation of sine, cosine, tangent, or cotangent, as the case 
may require, and the number thus given will be the one sought. 
If the angle is obtuse, we must make use of its supplement (§ 13). 

§ 36. When the angle is expressed in degrees, minutes, and 
seconds, we proceed as follows : 

Let it be required, for example, to find the logarithmic 



§ 36.] TRIGONOMETRY. 31 

sine of 13° 14' 17". By what has already been said, we read- 
ily find 

sin. 13° 14: = 9-359678 

sin. 13° 15' = 9-360215 



537 = diff. for 1'. 

Hence, 537 -r 60 = 8'95 = diff. for 1", and 895 » diff. for 100". 
If we suppose the logarithmic sines to increase in the same 
ratio as the increase of their corresponding arcs, which suppo- 
sition is very nearly correct, we shall be able to find the differ- 
ence corresponding to 17" by multiplying 8*95 by 17, which 
gives 152-15. 

sin. 13° 14' = 9-359678 

152 add. 



9-359830 = sine of 13° 14' 17". 

The column D, immediately at the right of the column of 
sines, gives the differences of the logarithmic sines for 100". 
Thus, in the tables opposite the sine of 13° 14' in the column D, 
we find 895, which we have already shown to be the increase 
for 100". In the same way, the column D, immediately after 
the column of cosines, gives the difference of the logarithmic 
cosines for 100". The column D, between the tangent and co- 
tangent columns, answers for both, giving also the difference 
for 100". 

Hence, to find the logarithmic sine of an arc given in degrees, 
minutes, and seconds, we must first seek the value correspond- 
ing to the degrees and minutes ; then multiply the correspond- 
ing tabular number in column D by the number of seconds, 
cutting off two places to the right for decimals ; add the product 
to the value already found, and the result will be the logarithmic 
sine sought. Thus, find the sine of 37° 31' 13". 

Sin. 37° 31' = 9-784612. Tabular number D = 274, which 
multiplied by 13, the number of seconds, gives 274 x 13=3562 ; 
pointing off two decimals, we have 35 - 62, or 36 nearly, which 
added gives 

sin. 37° 31' = 9-784612 

36 



sin. 37° 31' 13" = 9-784648 



32 TRIGONOMETRY. [CHAP. II. 

The tangent of an arc where there are seconds is found by 
the same method as has been employed for finding the sine. In 
finding the values of the cosine and cotangent, we must bear in 
mind that the cosines and cotangents decrease as the arcs in- 
crease, consequently the corrections found by aid of columns D 
must be subtracted instead of being added. 

Find the cosine of 23° 6' 47". 

cos. 23° 6' = 9-963704 

subtract 42*30= T \\ of 90 (D.) 

cos. 23° 6' 47" = 9-963662 

Find tangent and cotangent of 30° 30' 30". 
tang. 30° 30' = 9-770148 

add 144= T 3 /o of 481 (D.) 

tang. 30° 30' 30"= 9*770292 

cotan. 30° 30' =10-229852 

subtract 144= T W of 481 (D.) 

cotan. 30° 30' 30"=10'229708 

§ 37, To find the arc expressed in degrees, minutes, and sec- 
onds, when its logarithmic sine, cosine, tangent, or cotangent is 
given. 

Seek for the given value in the column having the proper 
designation of sine, cosine, tangent, or cotangent, as the case 
may require, keeping in mind (§ 34) that the columns desig- 
nated by sine and cosine at the top of the page are marked co- 
sine and sine respectively at the bottom of the page. Also, 
those marked tangent and cotangent at the top are respectively 
cotangent and tangent at the bottom. 

If the exact value is found in the table, the arc will be accu- 
rately given in degrees and minutes. The degrees are to be 
taken from the top of the page, and the minutes from the left- 
hand column, when the proper precept of the column is found 
at the top. But when the precept is found at the bottom, the 
degrees are to be taken from the bottom of the page and the 
minutes from the right-hand column. 

If the number cannot be exactly found in the table, then find, 
as above, the degrees and minutes corresponding to the nearest 



§ 38.] TRIGONOMETRY. 33 

less logarithm. Divide the difference of these logarithms, with 
two ciphers annexed, by the tabular difference taken from col- 
umn D, the quotient will give seconds, which seconds are to be 
added to the degrees and minutes already found, in the case of 
a sine or tangent, but to be subtracted in the case of a cosine or 
cotangent. 

EXAMPLES. 

1. Find the arc whose logarithmic sine is 9*365365. 

9*365365= given logarithmic sine, 
sin. 13° 24' = 9*365016 



349 = difference, 
and 34900 -r 883 = 38, the number of seconds. 
Hence, the arc 13° 24' 38" corresponds with the logarithmic 
sine of 9*365365. 

2. Find the arc whose cosine is 9*142857. 

9*142857 = given logarithmic cosine, 
cos. 82° V = 9*142655 



20200 -7- 1500 = 13". 
subtract 13" 



82° 0' 47" = arc required. 

3. Find the arc whose tangent is 10*528017. 

10*528017 = given logarithmic tangent. 



tang. 73° 29' =10*527931 



8600 -f- 772 = 11". 
add 11" 



73° 29' 11"-*= arc required. 

4. Find the arc whose cotangent is 9*555555. 

9*555555 = given logarithmic cotangent. 
cotan.70°14' =9*555536 



1900 -T- 661 = 3", nearly, 
subtract 3" 



70° 13' 57"= arc required. 

§38. The secants and cosecants are omitted in this table, 

3 



34 TRIGONOMETRY. [CHAP. II. 

since they are so readily found by the aid of the cosines and 
sines. By equation B, § 8, we have 

1 A 1 

sec. A = r ; cosec. A 



cos. A ' ' sin. A' 

Clearing of fractions, we have 

sec. A x cos. A = 1 ; cosec. A x sin. A = 1. 

Taking the logarithms, and observing to add 10 to each loga- 
rithm, we have 

log. sec. A +log. cos. A=20 ; log. cosec. A + log. sin. A=20. 

Hence, log. sec. A = 20 —log. cos. A, 

log. cosec. A = 20— log. sin. A. 

From this we see that 

The logarithmic secant isfou/nd by subtracting the logarithmic 
cosine from 20 ; and the logarithmic cosecant is found by sub- 
tracting the logarithmic sine from 20. 

EXAMPLES. 

1. Find the logarithmic secant and cosecant of 41° 41'. 

20- 20- 

sin. 41° 41'= 9-822830; cos. 41° 41'= 9*873223. 

cosec. 41° 41'=10\L77170 ; sec. 41° 41'=10-126777. 

2. What is the secant and cosecant of 15° 15' 15" ? 

20- 20- 

sin. 15° 15' 15"= 9420123 ; cos. 15° 15' 15"= 9-984423. 

cosec. 15° 15' 15"=10-579877 ; sec. 15° 15' 15"=10-015577. 

§39. Since we have (equation B, §8) tansr. A = 

x ' * ; & cotan.A' 

it follows that 

tang. A x cotan. A = 1, 
and log. tang. A + log. cotan. A = 20. 

Hence, the logarithmic cotangent may be found by subtract- 
ing the logarithmic tangent from 20 ; and, conversely, the loga- 
rithmic tangent may be found by subtracting the logarithmic 
cotangent from 20. 



§40.] 



TRIGONOMETRY. 



35 



EXAMPLES. 



1. The logarithmic tangent of an arc is 9*545454: ; what is the 
logarithmic cotangent of the same arc ? Ans. 10*454546. 

2. The logarithmic cotangent is 9*333444 ; what is that of the 
tangent of the same angle ? Ans. 10*666556. 



TABLE IV. 



TRAVERSE TABLE. 

§ 40. This table is of great assistance to the surveyor and 
navigator. 

If a line of a survey, as AB, make an angle BAC 
with the meridian !NS, the difference between the 
latitudes of the two extremities will be AC, and the 
difference between the longitudes of its two extrem- 
ities will be BC. Hence, AC is called the lati- 
tude and BC the departure of the line AB, which 
line is called the distance. The angle BAC is 
called the hearing. 

When the distance and bearing are given, we 
may find the latitude and departure as follows : 

By definitions, § 8, we have 

AC . . BC 



cos. A == 



AB 



sin. A 



AB' 



Clearing of fractions, we have 

cos. A x AB = AC ; sin. A x AB 



BC. 



(I*) 



By equations (1), the latitude and departure for any distance 
and bearing may be readily computed. In our table these values 
are given for distances from 1 to 100, for every quarter of a de- 
gree of the first quadrant. 

When the bearing is less than 45°, it will be found at the top 
of the page ; if greater, it will be found at the bottom. Dis- 
tances which do not exceed 50 are given on the left-hand page ; 
those exceeding 50 are to be found on the right-hand page. The 
columns marked latitude at the top are marked departure at 
the bottom ; those marked departure at the top are marked lat- 
itude at the bottom. 



36 TRIGONOMETRY. [CHAP. H. 

§ 41. When the number exceeds 100, we may separate it into 
units and tens, and find the latitude and departure of each part 
separately, and then take their sum. For example, suppose we 
wish the latitude and departure of the distance 317, the bearing 
being 19±°. 

317 = 310 + 7 = 31 xlO+7. 

Latitude, 

310 = 292-20 = ten times the latitude of 31. 
7 = 6-60 



317 = 298-80 

Departure. 

310 = 103*50 = ten times the departure of 31. 
7 = 2-34: 



317 = 105-84: 

When the distances are given in whole numbers and decimals, 
as, for example, in chains and links, we seek for the whole num- 
ber first, and afterwards for the decimal. 

Kequired the latitude and departure for a distance of 37-45, 
the bearing being 51 J°. 

Latitude. 

37 = 23-16 
0-45 = 0-28 = one-hundredth of the latitude of 45. 



37*45 = 23-44 

Departure. 

37 = 28-86 
0-45 = 0*35 = one-hundredth of the departure of 45. 

37-45 = 29-21 

EXAMPLES. 

1. Find the latitude and departure for a distance of 10-13 
chains, the bearing being 20i°. * ( 9-50 latitude. 

1 3*51 departure. 

2. Find the latitude and departure for 14*17 chains, the bear- 
ing being 75i°. A < 3-55 lat. 

" ( 13-71 dep. 

3. Find the latitude and departure for 3*65, the bearing be- 

2-79 dep. 



§42.] 



TRIGONOMETRY. 



37 



CHAPTEK m. 



SOLUTION OF RIGHT TRIANGLES. 



CASE I. 



§ 42. Given, the hypotenuse and 
one of the angles, to find the other 
parts. 

Suppose the given angle to be 
A. Then will the angle C be found 
by subtracting A from 90°. 

By our definitions' (§ 8), we have 




\ P A ^ 

sm. A = ~ : cos. A= T , 



which, cleared of fractions, give 

p = h sin. A. 
b = h cos. A. 



a.) 

(2-) 



By using logarithms, we have 

log. p = log. h + log. sin. A. . (3.) 
log. h = log. h + log. cos. A. . (4.) 

As an example, suppose the hypotenuse to be 125, and the 
angle at A to be 37° 30'. Required the other parts. 

A = 125; A = 37° 30'. 

We find C = 90° -37° 30' = 52° 30'. 



By Natural Numbers. (Table III.) 

sin. 37° 30' = 0-60876 ; cos. 37° 30' = 0*79335 
125 125 



304380 
121752 

60876 



76-09500 =p 



396675 
158670 
79335 

99-16875=5. 



38 



TRIGONOMETRY. 



[chap. m. 



By Logarithms. 



log. 125 =2-096910 . . . 2-096910 
log. sin. 37° 30' = 9-784447 ; log. cos. 37° 30' = 9-899467 



log. #=1-881357 
Hence, p = 76-095, and b = 99*169. 



log. b = 1-996377 



Note. — In adding the log. sin. and log. cos. respectively to the log. 125, we re- 
jected 10 from the sum to correct for the 10 which had been added to all logarithms 
of the sines, cosines, &c. (§ 34). 



CASE II. 



§ 43. Given, a side, that is, ei- 
ther the perpendicular or the base, 
and the angle opposite that side, to 
jmd the other parts. 

Suppose the given side to hep, A 
and the given angle A. Then will 
the angle C be the complement of A. 

By definitions (§ 8), we have 




sin. A = y ; cot. A = — , 
h p 1 



which readily give 



h 



P 



(1.) 
(2.) 



sin. A* 
b =p cot. A. . 

By using logarithms, we have 

log. h = log. p— log. sin. A. 

log. b =log.^>+log. cotan. A. . 

For example, suppose the perpendicular to be 75, and the 
angle at A to be 39° 15'. Required the other parts. 

^ = 75; A = 39° 15'. 

We find C = 90°-39° 15' = 50° 45'. 



(3.) 
(4.) 



§44.] 



TRIGONOMETRY. 



39 



By Natural Numbers. (Table III.) 
sin. 39° 15' = 0-63271 ; cotan. 39° 15' =1*22394 



0-63271 ) 75-00000 ( 
63271 


118-53 


= A. 


1-22394 

75 




117290 
63271 




540190 
506168 


611970 

856758 




340220 
316355 


91-79550 = 


= b. 


238650 
189813 





48837 

By Logarithms. 

log. 75 =1-875061 . . . . 1-875061 
log. sin. 39° 15' = 9-801201 ; log. cotan. 39° 15' = 10*087760 

log. h = 2-073860 log. b = 1-962821 

Hence, h = 118*54, nearly, and 5 = 91*795, nearly. 

Note. — In this example, before subtracting the log. of the sine of 39° 15' from 
the log. of 75, it was necessary to increase this logarithm by 10, since the logarithm 
of the sine had been increased by the same quantity. In the second operation, 
after adding the log. of the cotangent to the log. of 75, we rejected 10 from the 
sum, for the reason assigned in the last note. 



CASE III. 



§ 44, Given, a side, and the an- 
gle adjacent that side, to find the 
other parts. 

Suppose the given side to be b, 
and the given angle A. Then will 
the angle C be the complement 
of A. 




4:0 TRIGONOMETRY. [CHAP. in. 

By definitions (§ 8), we have 



which give 



cos. A = -7-; tang.A = ^r, 



A= — —r-. .... (1.) 

cos. A J 



p = h tang. A (2.) 

Using logarithms, we have 

log. h = log. J— log. cos. A. . . (3.) 
log. p = log. 5 + log. tang. A. . . (4.) 

For example, suppose the base to be 90*5, and the angle at A 
to be 50° 30'. Required the other parts. 

I = 90-5 ; A = 50° 30'. 
We find C =90° -50° 30' = 39° 30'. 

By Natural Numbers. (Table III.) 

cos. 50° 30' =0-63608 ; tang. 50° 30' =1-21310. 

0-63608 ) 90-50000 ( 142*27 = A 
63608 



268920 1-2131 

254432 90-5 



144880 60655 

127216 109179 



176640 109-78555 =p. 

127216 



494240 
445256 



48984 

By Logarithms. 

log. 90-5=1-956649 .... 1-956649 
log. cos. 50° 30' = 9-803511 ; log. tang. 50° 30' = 10*083896 

log. h = 2-153138 log. p = 2-040545 
Hence, h = 142-27, and p = 109-78. 



§45.] 



TRIGONOMETRY. 



41 



CASE IV. 



§ 45. Given, the hypotenuse and 
one of the sides, to find the other 
parts. 

Suppose the given side to be b, 
then (§ 8) we have 

sin. C = cos. A = 




JP 



(1-) 



or, using logarithms, 

log. sin. C = log. cos. A = log. b — log. h. . (2.) 

Again, from the fundamental property of the right triangle, 
we have 



hence 



52 +^2 = ^ 
p^ = h i -¥ = {h-\-b){h-b). 



(3.) 



p = V(h + b)(h-b). 
Using logarithms, we have 

log. jp = i [log. (A + b) + log. (h - b)l . (4.) 

For example, suppose the hypotenuse to be 112, and the base 
to be 97. Required the other parts. 

£=112; 6-97. 

112 ) 97-00000 ( 0-86607 = sin. C = cos. A. 
896 



740 
672 



680 

672 



800 
'784 

16 

Hence (by Table III.), C = 60° and A = 30°. 
Again, h + b = 209, and h — b = 15. 



42 



TRIGONOMETRY. 

Extracting Square Root. 



[chap. m. 



209 




5 


3135 , 


15 




105 


25 


1045 

209 




1109 
11189 


635 

525 


3135 






11000 
9981 




101900 








100701 




199 






By Logarithms. 


log. 


97 = 


= 1-986772 




log. 112 = 


= 2-049218 





( 55-99 =p. 



9-937554 =log. sin. C =log. cos. A. 
Hence, C = 60° 0' 19" ; A = 29° 59' 41 •'. 



Again, 



log. 209 = 2-320146 
log. 15 = 1-176091 

2 ) 3-496237 

log.jp = 1-748118 
Hence, p = 55*991 . 

CASE V. 



§ 46. Given, the two sides, to 
find the other parts. 



By § 8, we have 




_i> 



tang. A = cotan. C = 4r. . . 

or, using logarithms, 

log. tang. A = log. cotan. C = log.jp--log. b. 



a-) 

(2). 



§46.] TRIGONOMETRY. 43 

The hypotenuse is immediately deduced from 

A a =5 2 +^ 2 , 
which gives 

h = W +p\ . . . (3.) 

Since this last formula is not well adapted to the use of loga- 
rithms, we will remark that after having found the angles, by 
means of equations (1) or (2), we may then determine the hy- 
potenuse by Case II., equation (1), which gives 

log. li = log. p — sin. A. . . . (4.) 

As an example, suppose the base to be 83*5 and the perpen- 
dicular to be 62*25. Kequired the other parts. 

I = 83-5 ; p = 62-25. 

By Natural Numbers. (Table III.) 

83-5 ) 62-25 ( 0*74550 = tang. A = cotan. C. 
5845 



3800 Hence, A = 36° 42' 

3340 C = 53° 18' 



4600 
4175 



4250 
4175 



750 







62-25 =p 


83-5 = 6 




62-25 


83-5 




31125 


4175 




12450 


2505 




12450 


6680 




37350 


6972-25 = ¥ 


p 2 = 3875-0625 




: 104-15 : 


b 2 = 6972-25 




10847-3125 = J 2 +y. 


V10847-3125 = 


= h. 



44 TRIGONOMETRY. [CHAP. m. 



By Logarithms. 

log. 62-25 = 1-794139 
log. 83-5 = 1-921686 



log. tang. A = log. cotan. C = 9-872453 

Hence, A = 36° 42' 18" ; C = 53° 17' 42". 

Again, 

log. 62-25=1-794139 

log. sin. 36° 42' 18" = 9*776480 

log. 7i =-2-017659 
Hence, h = 104-15. 

§47. Additional Examples of Right Triangles. 

1. Given, the hypotenuse, equal 365, and one of the acute 
angles, equal 33° 12', to solve the triangle. 

The other angle = 56° 48'. 

< The sides ^ U99 * 86 - 



305-42. 

2. Given, one of the sides equal to 33*33, and the angle oppo- 
site this side = 83° 33', to solve the triangle. 

i The other angle = 6° 27. 
Ans. •] The other side = 3-768. 
( The hypotenuse = 33*542. 

3. Given, one of the sides equal to 105-5, and the acute angle 
adjacent this side equal to 46° 3', to solve the triangle. 

( The other angle = 43° 57'. 
Ans. \ The other side = 109*44. 
( The hypotenuse = 152*01. 

4. Given, the hypotenuse equal 111*1, and one of the sides 

equal 37*5, to solve the triangle. 

( The other side = 104*58. 

A**- i riu, i B (19° 43' 36". 

) The angles = < _ 

( & (70° 16' 24". 

5. Given, the two sides equal 29*37 and 37*29, to solve the 

triangle. ( The hypotenuse = 47*572. 

Ans - T1 i ( 38° 13' 28". 

/ Hie angles = { 

* & (51° 46' 32". 

The above examples have all been wrought by the use of 
logarithms, which is, as a general thing, more simple than by 



§49.] 



TRIGONOMETRY. 



45 



the use of natural numbers only. It will be well, however, for 
the pupil to apply both methods, as was done in the examples 
which followed immediately after each case ; by so doing, he 
will be the better prepared to comprehend the true nature of the 
trigonometrical values as well as their logarithmic values. 

§ 48. Hereafter, when we use the word sine, cosine, tangent, 
or cotangent, we wish to have it understood as meaning the log- 
arithms of those values, increased by 10, as given in Table II. 
"When we mean their real, or natural values, we shall say nat- 
ural sine, cosine, &c. These last values are given in Table III. 



CHAPTER IV. 

SOLUTION OF OBLIQUE TRIANGLES. 

§ 49, All the different cases of oblique triangles may be 
solved by the aid of the following theorems : 

THEOREM I. 

The sides of any plane triangle are to each other as the sines 
of their opposite angles. And conversely, the sines of the angles 
of any plane triangle are to each other as their opposite sides. 

In the triangle ABC denote 
the sides opposite the angles 
A. B, C, respectively by the 
letters a, b, c. Draw CD per- 
pendicular to AB, and we 

shall have (§ 8) 

CD 




■o CD 

sin. A = —j-, sin. B = ; 

o ' a 

dividing the first equation by the second, we have 

sin. A _ a 

sinTB""P 
which gives a : ~b : : sin. A : sin. B. . 

In the same way it may be shown that 

a : c : : sin. A : sin. C. . 



a-) 

(2-) 
(3.) 



46 



TRIGONOMETRY. 



[chap. rv. 




THEOREM II. 

In any plane triangle, the sum- of 
amy two sides is to their difference as 
the tangent of half the sum of the op- 
posite angles is to the tangent of half 
their difference. 

By Theorem I., we have 

o : c : : sin. B : sin. C ; 

hence, by composition and division, we have 

o + c : o— c : : sin. B + sin. C : sin. B — sin. C, 

which gives 

o -\-c _ sin. B -|- sin. C 
o—c sin. B — sin. C 

By equation (9), § 16, we have 

sin. B + sin. C _ tang, i (B + C) 



(1.) 



sin. B — sin. C tang, i (B— C)' 



Hence, we have 



b+c _ tang. HB + C) 
&-c~"tang.f(B-C)' 



(2.) 



or. 



b + c : b-c : : tang. \ (B + C) : tang. J<B-C). (3.) 



THEOREM III. 

If from an angle of a plane 
triangle a perpendicular be 
drawn so as to meet the opposite 
side or base, the whole- base will 
be to the sum of the other two 
sides as the difference of those 
sides is to the difference of the 
segments of the base. 

Drawing CD perpendicular to AB, we have 

& 2 = AD 2 + CD 2 
a 2 = BD 2 +CD 2 . 




(1.) 
(2.) 



§50.] 



TRIGONOMETRY. 



4:7 



or 



Subtracting (2) from (1), we have 

tf-a? = AD 3 -BD 2 , 

(5 + a) (b - a) = (AD + BD) (AD - BD), . (3.) 



which, converted into a proportion, will give, observing that 
AD + BD = & 



c : h+a : : o-a : AD-BD. 



(4.) 



K the triangle has an obtuse angle, then the perpendic- 
ular should be drawn from this obtuse angle, otherwise it 
will not meet the opposite side. The theorem might be so 
modified as to embrace this case ; but as it is used only in the 
solution of a triangle when the three sides are given, such mod- 
ification is unnecessary. 

§ 50. The solution of all oblique triangles may be included 
in four cases, as follows : 

CASE I. 

Given, a side and two angles, to find the other parts. 

Since the sum of the three angles 
of any plane triangle is equal to 180°, 
the third angle may be found by sub- 
tracting the sum of the two given an- 
gles from 180°. Having all the an- 
gles, the two remaining sides may be 
found bv Theorem I. Thus, if we 
suppose the side c to be given, we 
shall have 

sin. C : sin. A : : 

sin. C : sin. B : : 




which give 



a, 



a — 



h = 



c sin. A 

sin. C 
g sin. B 



sm. (J 

Using logarithms, we have 

log. a = log. c + log. sin. A— log. sin. C. 
log. b = log. g + log. sin. B —log. sin. C. 



a-) 

(2.) 



(3.) 



48 TRIGONOMETRY. [CHAP. IV. 

By using arithmetical complements (§ 32), we shall have 

log. a= sly. co. log. C + log. sin. A + log. c (5.) 

log. b = ar. co. log. C + log. sin. B + log. c . (6.) 

As an example, suppose the angle A = 30° 20', the angle 
B = 50° 10', and consequently the angle C = 99° 30'. If the 
side g is 93*37, what will be the lengths of the other sides ? 

Using equations (5) and (6), we have 

ar. co. sin. 99° 30' (80° 30') = 0*005997 . . 0*005997 

sin. 30° 20' =9*703317; sin. 50° 10'=9*885311 

log. 93*37 = 1*970207 . . 1*970207 

log. a = 1-679521 log. 5=1*861515 

Hence, a = 47*81 ; b = 72*697. 

Note. — Since the angle C = 99° 30' is an obtuse angle, we subtract it from 180, 
and obtain its supplement 80° 30', the sine of which is 9'994003. Now subtracting 
this from 10, we have O , 00599'7 for the arithmetical complement of the logarithmic 
sine of 99° 30'. 

The arithmetical complement may be readily taken from the table, by beginning 
at the left hand, and subtracting each figure from 9, except the last significant 
figure on the right, which must be subtracted from 10. (§ 32.) 

CASE II. 

Owen, two sides and an angle opposite one of them, to find 
the other parts. 




Suppose the sides a and b to be given, and the angle A op- 
posite the side a. 

By Theorem I., we have 

a : b : : sin. A : sin. B, 

OT* • -n ^ Sin. jDL /h v 

U1 » sin. B = . . . . (1.) 

a 

Using logarithms, we have 

log. sin. B = ar. co. log. a + log. b + log. sin. A. (2.) 

Having thus found the second angle, the third angle at C 
may be obtained by subtracting the sum of these two from 180°. 



§ 50.] TRIGONOMETRY. 49 

Then by Theorem I., we have 

sin. A : sin. : : a •: e, 

a sin. C , n . 

or, c = — -. t— , .... (3.) 

sin. A ' w 

which by logarithms, becomes 

log. c = ar. co. log. sin. A + log. sin. C + log. a. (4.) 

Scholium. In equation (1), the numerator, b sin. A, is the 
perpendicular CD ; now if a is less than this perpendicular, 

the value of the fraction - — , which gives the sine of B, 

will exceed a unit, which is impossible. But while a is greater 
than this perpendicular, and does not at the same time exceed 
5, there will be two solutions, as represented in the two dia- 
grams. When there are two solutions, the angle at B in the 
second triangle will be the 'supplement of the angle at B in the 
first. 

As an example, suppose the side a — 75*5 and the side b = 
98*5 ; and suppose the angle at A to be 37° 37', required the 
other parts. 

By equation (2), we have 

ar. co. log. 75-5 = 8-122053 

log. 98-5 = 1-993436 

log. sin. 37° 37' = 9-785597 

log. sin. B = 9-901086 

Hence, B = 52° 46' 48", consequently the angle at C = 
89° 36' 12". 

Now, by equation (4), we have 

ar. co. log. sin. 37° 37' == 0-214403 

log. sin. 89° 36' 12" = 9-999989 

log. 75-5 = 1-877947 

log. o = 2-092339 
and c = 123-69. 

The above solution corresponds Avith the first figure ; if we 
take 127° 13' 12" for the angle at B, which is the supplement 

4 



50 



TRIGONOMETRY . 



[CHAP. IY. 



of 52° 46' 48", we shall then find 15° 9' 48" for the angle at C. 
Then, by equation (4), we have 



ar. co. log. sin. 37° 37' = 0-214403 
log. sin. 15° 9' 48" = 9-417590 

W. 75-5 = 1-877947 



log. c = 1-509940 



and c = 32-355. 
This second solution corresponds with the second figure. 



CASE III. 



Given, two sides and the included angle, to find the other 
parts. 

Suppose the sides b and c, with 
the included angle A, to be given. 

By subtracting the angle A from 
180°, which is the sum of the three 
angles, we have 



and 



B + C=180°-A. 




£ (B + C) = 90° - \ A = complement of h A. 

Then by Theorem II., we have 

b-\-c : b—G : : cotan. \ A : tang. J(B — C), 

which gives 

_{b—c) cotan. -| A 



b + c 



(1.) 



tang.i(B-C) 

Using logarithms, we have 

log. tang. -J (B— C) = ar. co. log. (b + c) + log. (b—c) + log. co- 
tan. \ A. .... (2.) 

Having thus found half the difference of the angles B and C, 
we add it to half their sum, and thus obtain the greater angle, 
which must be opposite the greater side. The smaller angle is 
found by subtracting half their difference from their half sum. 

Again, having found all the angles, we have, by Theorem L, 



or. 



sin. B : sin. A : : b : a, 
b sin. A 



a = 



sin. B 



(3.) 



50.] 



TRIGONOMETRY. 



51 



Using logarithms, we have 

log. a — ar. co. log. sin. B -f- log. sin. A + log. b. (4.) 

As an example, suppose the side b = 50:24, and the side o = 

43'25, and suppose the angle A to be 40° 15', required the other 

parts. 

A = 40° 15' ; I = 50-24 ; c = 43*25, ' 

consequently, 

I + c = 93-49; &-.<? = 6-99; \ A = 20° V 30". 

Equation (2) gives 

ar. co. log. 93-49 = 8-029235 

log. 6-99= 0-844477 

los:. cotan. 20° 7' 30" =10-435993 



log. tang, i (B-C) = 9-309705 
And i (B - C) = 11° 31' 55" 
i (B + C) = 69^ 52' 30" 

B = 81° 24' 25" = sum. 

C = 58° 20' 35" = difference. 

By equation (4), we have 

ar. co. loo;, sin. 58° 20' 35" = 0-069965 

= 9-810316 
1-635986 



log. sin. 40° 15' 



log. 43-25 



log. a = 1-516267 
And a = 32*829. 



CASE IV. 



Given, the three sides, to 
find the angles. 

If we conceive CD to be 
drawn perpendicular to the 
side <?, we shall have, by The- 
orem III., 




c : b + a : : b-a : AD-BD, 
AV-BDJ h + a){h - a \ 



- • (1.) 
log. (AD-BD)=ar. co. log. c+log. (b +a) -flog. (b-a). (2.) 



Using logarithms, we have 



52 TRIGONOMETRY. [CHAP. IV. 

This gives half the difference of the segments AD and BD ; 
if we add this half difference to the half sum, that is, add it to 
half of c, we shall obtain AD, the greater segment. The half 
difference subtracted from the half of c will give BD, the 
shorter segment. 

Then solving the two right triangles ADC and BDC, by- 
Case IV. of Right Triangles, we have 

. AD ^ BD 

cos. A =— T - : cos. B = . 

b a 

Using logarithms, 

log. cos. A = log. AD— log. 5, . . (3.) 

log. cos. B =log. BD— log. a. . . (4.) 

Having found the angles A and B, subtract their sum from 
180° for the third angle C. 

For example, suppose we have a — 50*25 ; h = 60*5, and 
<y= 68*4. Required the angles. 

b + a = 110-75 ; b-a = 10*25. 

By equation (2), we have 

ar. co. log. 68-4 = 8*164944 
log. 110*75 = 2*044344 
log. 10*25=1*010724 

log. (AD-BD) = 1*220012 
AD-BD = 16*596 

| c + \ (AD-BD) = 42*498 = AD. 
\ o -i (AD -BD) = 25*902 == BD. 

By equations (3) and (4), we have 

log. 42*498 = 1*628369 ; log. 25*902 = 1*413333 
log. 60*5 = 1*781755 ; log. 50*25 = 1*701136 



log. cos. A = 9*846614 ; log. cos. B = 9*712197 
Hence, A = 45° 22' 35" ; B = 58° 58' 18". 
Consequently, C — 75° 39' 7". 

Perhaps a better method for this case would be as fol- 
lows : — 



or, 



§ 50.] TRIGONOMETRY. JS3 

If to equation (1), which is 

AD-BD=— -, 

G 7 

we add 

AD + BD=<?, 

we shall have 

G 7 

hence, 

. AD ^-t-c 2 -^ /K . 

C0B ' A= -r=-^YG— ■ • (5 -> 

Adding 1 to each member of (5), we have 

1 + cos. A = 1 + -2j— = 2To , 

l + co S .A = {h + C + ^ o +e - a \ . (6.) 

Denoting half the sum of the three sides by s, we have 
b-\-c + a = 2s m , h-\-G — a = 2s — 2 a — 2 (s—a). 
Hence equation (6) will become 

1 +,cos. A = — ^ '-. . . (7.) 

By equation (8), § 15, we have 

1 + cos. A = 2 (cos. \ A) 2 . 
Therefore equation (7) will become 

2(co,iA)-^-i^), 

(00,^ = 1^; 
consequently, 



cos. I A = s/*JLz£. 

be 



In a similar manner, we find 



..B=v/*-^=4 - • (9.) 



COS 

ac 



cos. i C = \Z " {s ~ °\ . . (10.) 



54: TRIGONOMETRY. [CHAP. TV. 

By using logarithms, equations (8), (9), and (10) become 

log. cos. J A=i [ar. co. log. 5+ar. co. log. c+log. s+log. (s—a)] 1 
log. cos. J B= J [ar.co. log.«+ar. co.log.c+log.s+log. (s—b)] }-(A) 
log. cos. \ C=J [ar. co. log. a+ar. co. log. 5+log. s+log. (s— c)] J 

Applying equations (A) to the case already given, we have 

a=50-25; 5=60-5; c=68*4; 
consequently, 

i (a + b + c) = s = 89-575, and s- a = 39*325; 5-5 = 29-075; 

s-c = 21-175. 



ar. co. log. 5 = 8-218245 ; ar. co. log. a = 8-298864 

ar. co. log. c = 8-164944 ar. co. log. c = 8-164944 

log. s = 1-952187 log. s = 1-952187 

log. (s-a) = 1-594669 log. (s-b) = 1-463520 

2)19-930045 2)19*879515 



log. cos. |A= 9-965022 log. cos. | B = 9*939757 

ar. co. log. a = 8-298864 

ar.co. log. b= 8-218245 

log. s= 1-952187 

log. (s-c) = 1-325823 

2 ) 19-795119 

log. cos. JC= 9-897559 

Hence \ A = 22° 41' 17" ; \ B = 29° 29' 9" ; \ C=37° 49' 34", 
and A = 45° 22' 34" ; B = 58° 58' 18" ; C = 75° 39' 8". 

When the sides of a triangle are expressed in small numbers, 
equation (5) may be advantageously employed : this equation, 
when the letters are properly permuted so as to apply to each 
angle, gives 

b 2 -\- a* — a 2 



Nat. cos. A = 
ISTat. cos. B = 
Nat. cos. C = 



2 bo 
cP + c 2 — 


■ b 2 


2 ac 
a 2 +b 2 - 


-c 2 



2a5 



■ (B.) 



2x7x9 


126' 


25+81-49 


57 


2x5x9 


90' 


25 + 49-81 


-7 


2x5x7 


70* 


log. 57 = 


= 1-755875 


losj. 90 = 


= 1-954243 



§ 51.] TRIGONOMETRY. 55 

As an example, suppose the sides to be 5, 7, and 9. He- 
quired the angles. 

a = 5-, b = 7 ; o = 9. 

49 + 81-25 105 
JNat. cos. A = 



Nat. cos. B = 

Nat. cos. C = 

log. 105 = 2-021189 
log. 126 = 2-100371 

cos. A = 9-920818 cos. B = 9-801632 

log. -7 = 0-845098™ 
log. 70=1-845098 

cos. C = 9-000000^ 
Hence, A = 33° 33' 27" ; B = 50° 42' 13" ; C = 95° 44' 21". 

Note. — In taking the logarithm of —7, we took it as though it had been +7, and 
at the right annexed the letter n to indicate that the number is negative. So in 
the value of cos. C we write the n, thus indicating that the natural cosine of this 
angle is negative. We then seek in the tables for the angle as though its cosine 
was positive, and find 84° 15' 39", which taken from 180° gives the obtuse angle 
95° 44' 21" for the true value of C. 

§51. Additional Examples of Oblique Triangles. 

1. Given, two angles of a triangle equal 47° 13' and 63° 36', 

and the side opposite the first angle equal 27*5, to solve the 

triangle. ( The other angle — 69° 11'. 

Ans - L A '.j J 33-562. • 

1 The other sides = < 
I ( 35-024. 

2. Given, two sides of a triangle equal 47*13 and 63*36, and 
the angle opposite the first side equal 27° 50', to solve the tri- 
angle. ( The other side = 92*719. 

First Ans. \ j 38° 52' 47". 

lbe other angles — < 
' s 1 113° 17' 13". 

r The other side = 19*341. 

Second Ans. \ ™ ,, , j 141° 7' 13 v '. 

| The other angles - j n o 2 , ± v , 



56 TRIGONOMETRY. [CHAP. IV. 

3. Given, two sides of a triangle equal 49*5 and 101*5, and 
the angle opposite the first side equal 30° 25', to solve the tri- 
angle. Ans. The question is impossible. 

4. Given, two sides of a triangle equal 630 and 800, and the 
angle opposite the first side equal 100°, to solve the triangle. 

Ans. The question is impossible. 

5. Given, two sides of a triangle, 77*5 and 90*25, and the in- 
cluded angle equal 83° 38', to solve the triangle. 

i The other side = 112*25. 

^*w- •< mi + t i (43° 19' 38". 

J lhe other angles = < 

( 5 (53° 2' 22". 

6. Given, the three sides of a triangle, 40, 50, and 60, to find 
the angles. c 41° 24' 35". 

Ans. The angles == J 550 45/ 16". 

( 82° 49' 9". 

7. Given, two sides of a triangle, 100 and 90, and the angle 
opposite the first side, 111° 15', to solve the triangle. 

t The other side =21*823. 

Ans. < m, ' .1 1 ( 11° 44' 7". 

) lhe other angles = < 

( & I 57° 0' 53". 

8. In an obtuse-angled triangle one of the acute angles is 
29° 15', the other acute angle is 2° 45' ; the side opposite the 
first angle is 6*3. What are the other parts ? 

t The obtuse angle = 148°. 

Am ' The other sides = i °' 619 ' 
( I 6*832. 

9. Given, two sides of a triangle, 232*21, 237*61, and their 
contained angle equal to 72° 29' 48", to find the other parts. 

Ans. j The other an S les = J 66° 30' 37"i 
( The other side = 345*46. 

10. The three sides of a triangle are 10, 15, and 20. What 
are the angles ? r 28° 57''18". 

Ans.) 46° 34' 3". 
( 104° 28' 39". 

11. The three sides of a triangle are 123*48, 135*61, 140*91. 
What are the angles ? / 53° 0' 10". 

- Ans. < 61° 17' 50". 
( 65° 42' . 



§ 53.] MENSURATION. 57 

12. Two sides of a triangle are 59*34 and 12*13, and their in- 
cluded angle 150° 38'. What are the other parts ? 

A l ( 24° 30' 12". 

Anm.es 



Ans. < ^>=> x ™ • } 4° 51' 48". 

Side = 70*165. 



CHAPTER V. 



MENSURATION OF SURFACES. 



§ 52. The area of a surface is found by comparing it with 
some known and fixed surface, which is taken as the unit sur- 
face, which unit surface is usually in the form of a square ; as, 
a square inch, a square foot, a square yard, &c. 

The superficial unit receives its name from that of the linear 
unit, which measures its side. Thus, a square whose side is 
one inch is called a square inch ; one whose side is one foot is 
called a square foot ; one whose side is one yard is called a 
square yard. 

There are some superficial units which nave no correspond- 
ing linear unit, such as the acre, in land measure, and its fourth 
part, called a rood. There is no such linear measure as an acre 
or a rood. It would be absurd to speak of an acre long or a 
rood long. 

The usual units of square measure are given by the following 

TABLE OF SQUARE MEASURE. 



sq. inches. 


sq.feet. 






144 = 


1 


sq. yd. 




1296 = 


9 = 


1 


sq. rd. 


39204 = 


272} = 


30} = 


1 sq. ch's. 


627264 = 


4356 = 


484 = 


16 = 1 Acres. 


3272640 = 


43560 = 


4840 = 


160= 10= 1 8.M. 



4014489600 = 27878400 = 3097600 = 102400 = 6400 = 640 = 1 

§ 53. In measuring land, Gunter's Chain is most commonly 
employed. Its length is 4 rods, or 66 feet, and is divided into 
100 links, so that we have as follows : 



58 MENSURATION. [CHAP. V. 

7 r 9 o 2 F inches, or 7*92 inches = 1 link. 

100 links=792 inches=66 feet=22 yards=4 rods= 1 chain. 

80 chains = 1 mile. 

# 

10000 sq. links =.- 16 sq. rods == .... 1 sq. chain. 
100000 sq. links = 10 sq. chains = 160 sq. rods = . 1 acre. 

The unit of measure for land is the acre. It cannot be given 
in an exact square, since it is made to consist of 160 square 
rods, and 160 is not a square number, which proves that the 
side of a square containing 160 sq. rods cannot be accurately 
expressed in rods ; and if not in rods, then not in any multiple 
or submultiple of rods. 

One-fourth of an acre is called a rood, and the square rod in 
land measure is frequently called & perch. 

§ 54. If links be multiplied by links, the product will be 
square links, which may be reduced to acres by dividing by 
100000, or by simply pointing off five decimal places. If chains 
be multiplied by chains, the product will be square chains, 
which may be reduced to feres by dividing by 10, or pointing 
off one decimal figure. If chains are multiplied by links, the 
product will be converted into acres by pointing off three de- 
cimals. 

We will also add, that to convert square feet into acres, we 
must divide by 43560. To convert square yards into acres, we 
must divide by 4840 ; and to convert square rods into acres, we 
must divide by 160. 

JPROBLEM I. 

To find the area of a square or rectangular piece of land. 
The obvious rule in this case will be as follows : 

Take the product of two adjacent sides for the area. [Geom., 
33. IV., Prop. II., Scholium.] 

EXAMPLES. 

1. How many acres in a piece of ground in the form of a 
square, each of whose sides is 13 chains, 25 links, or 13*25 
chains ? 

13-25 x 13-25 = 175-5625 sq. chains. 



§54] 



MENSURATION". 



59 



Or, since 13*25 chains = 1325 links, we have 

1325 x 1325 = 1755625 square links, 
and 17*55625 = the number of acres. 

Converting this decimal of an acre into roods and perches, 

we have 

0-55625 

4 



roods = 2-22500 
40 



Ans. 11 A. 27?. 9P. 



perches = 9-00000 

2. How many acres in a rectangular piece of land whose ad- 
jacent sides are 30*25 chains and 25*21 chains ? 

2521 x 3025 = 7626025 sq. links = 76 A. IB. 1 T %\P. 

3. How many rods in a rectangular piece of ground 282 feet 



wide and 325 feet long ? 



Ans. 336*639 sq. rods. 




E 




PROBLEM II. 

To find the area of a parallelogram. 

FIRST RULE. 

When the altitude is given, 
multiply it by the base, for the 
area. [Geom., B. IV., Prop. III.] 

If we multiply AD by the sine 
of the angle at A, we shall ob- A 
tain DE. (Case L, Eight Tri- 
angles.) That is, 

DE = AD x sin. A, 

and area ABCD = DE x AB = AD x AB x sin. A. 

Using logarithms, 

log. area = log. AD + log. AB + log. sin. A— 10. 

We subtract 10 to correct for the 10 added to log. sin. of A. 
Hence we have this 

SECOND RULE. 

* 

Multiply the product of two adjacent sides by the natural sine 
of the included angle. 



a-) 

(2.) 



60 MENSURATION. [CHAP. V. 

Or by Logarithms. 

To the sum of the logarithms of two adjacent sides add the 
logarithmic sine of the included angle, and subtract 10, and the 
result will be the logarithm of the area. 

EXAMPLES. 

1. How many acres in a field in the form of a parallelogram, 
having a base of 13 chains 14 links, and an altitude of 10 chains 
37 links ? 1314x1037=1362618 sq. links=13JL 2i?. 20P. 

2. How man}' acres in a field in the form of a parallelogram, 
the adjacent sides being 25*17 chains and 30*25 chains, and 
having 70° 30' for the included angle ? 

By Logarithms. 

log. 25*17 = 1*400883 
log. 30*25 = 1*480725 
sin. 70° 30' = 9*974347 



log. area = 2*855955 

Hence, area = 717*72 sq. chains, which is 

Ans. 11A. 37?. S\P. 
3. A field, in the form of a parallelogram, has 10*21 chains, 
12*12 chains for the adjacent sides, and 30° 45' for the included 
angle. How many acres does it contain ? 

Ans. 63*27 sq. chains. 

PROBLEM III. 

To find the area of a triangle. 

FIRST RULE. 

When the altitude is given, multiply its half by the base. 
[Geom., B. IV. Prop. IV.] 

Or multiply the altitude by ^ n 

half the base, or take half the 
product of the altitude and base. / 

Since the triangle ABD is ob- / 
viously just one-half of the par- A 



§ 54.] MENSURATION. 61 

allelogram ABCD, whose measure is given by equation (1) of 
Prob. II., we obviously have 

. ^.^ DE x AB AD x AB x sin. A /H . 

area ABD = = ■ -. (1.) 

Or, using logarithms, 

log. area = log. AD + log. AB + log. sin. A -10-301030. (2.) 

The log. of 2, the denominator of (1), being 0*301030, is to 
be subtracted in addition to the 10. 
Hence, we have this 

SECOND RULE. 

Multiply the product of any two adjacent sides by the sine of 
the included angle, and one-half this last product will be the area. 

BY LOGARITHMS. 

To the sum of the logarithms of any two 'adjacent sides 
add the logarithmic sine of the included angle, and subtract 
10*301030 ; and the remainder will be the logarithm of the area. 

We have also given [Geom., B. II., Art. 59] a demonstration 
to this 

THIRD RULE. 

Take half the sum of the three sides, and from this half sum 
subtract each side separately / then take the square root of the 
continued product of the half sum and the three remainders, 
and it will be the area. 

BY LOGARITHMS. 

Find the half sum of the three sides, and the three remain- 
ders as before i take half the sum of their logarithms, and it 
will be the logarithm of the area. 

EXAMPLES. 

1. How many square feet in a triangle whose base is 110*5 
feet and altitude 97*25 feet ? 

Ans. i of 110*5 x 97*25 - 5373*0625 sq. feet. 

2. If an angle of a triangle is 33° 33', included by sides whose 



62 MENSURATION. [CHAP. V. 

lengths are 45*25 feet and 37*5 feet respectively, what will be 
its area in square rods ? 

log. 45-25 =1-655619 
log. 37-5 = 1-574031 
sin. 33° 33'= 9-742462 



12-972112 
10-301030 



2*671082 =log. of sq. feet, 
subtract 2*434968=log. of 272J, sq.ft. in a sq. rd. 

0*236114=log. of sq. rods. 

Ans. 1*7223 sq- rods. 

3. How many acres in a triangular field whose sides are 70, 
110, and 120 chains, respectively ? 

} of (70 + 110 + 120) = 150, log. = 2-176091 
150— 70 = 80, log. = 1-903090 
150-110 = 40, log. = 1-602060 
150-120 = 30, log. = 1-477121 

2)7-158362 

log. area = 3*579181 
Ans. 3794*7 sq. chains = 379*47 acres. 

4. How many sq. feet in a triangle, each of whose sides is 

denoted by a ? . , n * ,_ 

Ans. V^ax^ax^axla=—\/3. 

5. Referring to the last example, how many sq. feet in an 
equilateral triangle whose side is 10 feet? 

Ans. 43*301 sq. feet. 

PROBLEM IV. 

To find the area of a trapezoid. 



D E C 

RULE. 



Multiply half the sum of the 
'parallel sides by the perpendicidar 
distance between them. [Geom., A F 

B. II, Prop. \Y.] 



M.] 



MENSURATION. 



63 



EXAMPLES. 

1. What is the area of a trapezoid, whose parallel sides are 

20 and 30 chains, and which are perpendicularly distant 12*5 

chains ? 

\ of (20 + 30) = 25 ; 

25 x 12-5 = 312-5 sq. chains, or 

31 £ acres. 

2. If the parallel sides of a trapezoid, whose lengths are 25 
and 35 feet, are at the distance of 12 feet from each other, what 
will be its area? Arts. 3G0 sq. feet. 

3. What is the area of a trapezoid, whose parallel sides are 
3 and 4*90 chains, and the perpendicular distance between them 
1-68 chains? Ans. 6'557 sq. chains. 

4. How many square feet in a trapezoidal table whose par- 
allel sides are 5'5 feet and 4*25 feet, the width being 3'5 feet ? 

Ans. 17-0625 sq. feet. 

ScnoLiuM. — In land surveying, we frequently have occasion 
to measure long irregular portions of a field, which are bounded 
on one side by a straight line. 

At equal intervals along the 
straight line AF, as at B, C, D, and / 
E, measure the perpendiculars B&, 
Cc, D^, &c. ; also measure the ex- 
treme perpendiculars Ka and Yf. 
When the equal intervals AB, BC, 

CD, &c, are short, the figures AB&#, BCc5, CD<rZ<?, &c., may, 
without much error, be regarded as trapezoids ; hence, calling 
s one of the equal distances, AB, BC, CD, &c, we have 




area ABba = 



area BCcb — 



area CDde 



area Y>Yed — 



area YYfe 



Ka + Bb 


2 
Bb + Cc 

2 
Cc + Bd 


2 
Dd + Ye 


2 
Ye + Yf 



X 5, 



X $, 



X S< 



X 5, 



X S. 



The total area is (J- Aa + Bb + Cc + D^ + Ed + J Yf) x 5. 



64 



MENSUKATION. 



[CHAP. V. 



Hence this 



RULE. 



To half the sum of the extreme breadths add all the interme- 
diate breadths / multiply this sum by one of the equal distances, 
and the product will be the area. 

As an example, suppose seven breadths of an irregular field, 
taken at equal intervals, to be 32 links, 47 links, 63 links, 13 
links, IT links, 5 links, and 2 links ; if one of the equal inter- 
vals is 10 links, what will be the area ? 

qo i_ o 

— £-+ 47 + 63 + 13 + 17 + 5 = 162, 

and 162 x 10 = 1620 for the number of square links in the area. 

problem v. 
To find the area of any irregular polygonal figure. 

RULE. 

Draw a sufficient number of diagonals to divide the whole 
figure into triangles. Then compute each triangle separately, 
and take their sum. 

As an illustration, suppose ABCD 
EF to be the polygon. Draw the di- 
agonals EA, EB, EC, and suppose by 
actual measurement we find AB = 
12-5 ; BC = 11-25 ; CD = T ; DE = 
6-T5 ; EF = 5-75 ; FA = 10-5 ; EA = 
10-75 ; EB = 10 ; EC = 9-75. 

Now computing each triangle by a 
the Third Rule under Problem III., 
we shall find 

AreaEFA= 29-3795 
EAB= 51-6642 
EBC = 45-6431 
ECD= 23-6247 




u 



u 



area ABCDEF = 150-3115 



§54.] 



MENSUKATION. 



65 




PROBLEM VI. 

To find the area of a quadrilateral in terms of its diagonals 
and their included angle. 

Let ABCD be the quadrilat- 
eral figure, of which the diago- 
nals AC, BD, and their angle 
K of intersection are given. 

Through A, B, C, D, draw 
lines parallel to the diagonals, 
which will together form the 

parallelogram EFGH, whose angles are equal to the angles at 
K ; and whose area is obviously double that of the quadrilateral 
ABCD. 

But, Prob. II., EFGH = HE x HG x sin. H = BD x AC x 
sin. K ; and we have ABCD = ^ BD x AC x sin. K. 

Hence we have this 

RULE. 

Multiply the product of the two diagonals by the sine of their 
included angle, and one-half this last product will he the area. 

BY LOGARITHMS. 

To the sum of the logarithms of the two diagonals add the 
logarithmic sine of their included angle, and subtract 10-301030 ; 
and the remainder will give the logarithm of the area. 

Note. — This rule will agree with the second rule of Prob. Ill, if the word diag- 
onals is changed into sides. 

EXAMPLES. 

1. The diagonals of a quadrilateral are 37*5 and 46*25, and 

the j make with each other an angle of 47° 47'. What is the 

area? 

log. 37-5 = 1-574031 

log. 46-25 =1-665112 

sin. 47° 47' = 9-869589 



13-108732 
10-301030 



log. area = 2-807702 

and area = 642*247. 

5 



66 



MENSURATION. 



[CHAP. V. 



2. The diagonals of a quadrilateral are 90 and 100, and make 
an angle of 75° with each other. What is the area ? 

Arts. 4346 -6S, 



PROBLEM VII. 



To find the area of any regular polygon. 



FIRST RULE. 



Take one-half the product of the perimeter and perpendicular 
drawn from its centre to one of its sides. [Geom., B. V., 
Prop. VIII.] 

When the perpendicular is not given, 

it may be found as follows : the angle 

ACB will be found bv dividing 360° bv 

the number of sides in the polygon ; 

and the angle BCD, which is one-half 

of ACB, can be found by dividing 180° 

by the number of sides. Hence if we 

denote the number of sides by n, we 

180° 
6hall have , for the an^le BCD. 

» , 

Now BD, which is one-half of a side of the polygon, being mul- 
tiplied by cotan. BCD, will give CD. If, then, s denote a side 
and^> the perpendicular, we shall have 




P 



\ of s x cotan. 



180° 



n 



a) 



And, the perimeter being n x s, we shall obtain 
area = \ of p x n x s = J of s* x n x cotan. 



180° 



n 



(2-) 



If the side of the polygon is taken as a unit, then s = 1, and 

180° 



area 



= i of n x cotan. 



n 



(3.) 



If, in formula (3), we take successively n = 3, 4, 5, 6, 7, &c, 
we shall obtain the areas of regular polygons, whose sides are 
unity, as given in the following 



§54.] 



MENSURATION - . 



67 



TABLE. 



Names. Sides, 

Triangle 3 

Square 4 . . . . 

Pentagon 5 1 

Hexagon 6 

Heptagon 7 

Octagon 8 4 

Nona^on 9 6 

Decao-on 10 7 

Undecaofon 11 9 



Areas. Logarithms. 

•43-301 27...... T-6365007 

•0000000 0-0000000 

•7204774 0-2356490 

•5980762 0-4146519 

•6339124 0-5603744 

•8284271 0-6838057 

•1818242 0-7911166 

•6942088 0-8861640 

•3656399 O'97l537o 

Dodecagon 12 11-1961524 1*0490687 

Since the areas of similar figures are to each other as the 
squares of their homologous sides, we may find the area of any 
regular polygon whose number of sides is not greater than 12 
by this 

SECOND RULE. 

Multiply the square of the length of a side of the polygon foj 
the area of a similar polygon whose side is unity ^ as found in 
the preceding table. 

BY LOGARITHMS. 

To twice the logarithm of a side of the given polygon add the 
logarithm of the corresponding tabular number. 



EXAMPLES. 

1. What is the area of a regular dodecagon whose side is 7*75 ? 

log. 7-75 - 0-889302 

log. 7-75 = 0-889302 

tabular log. = 1-049009 



log. area = 2-827673 
Area = 672-469. 

2. "What is the area of an octagonal room, each side of which 
is 105 feet ? Ans. 532-334 sq. feet. 

3. What is the number of square inches in a pentagon, each 
of whose sides is 10 inches ? Ans. 172*048 sq. inches. 

4. What is the area of an equilateral triangle, having 100 for 
aside? Ans. 4330-127. 



68 MENSURATION. [CHAP. V. 

PROBLEM VIII. 

To find the circumference of a circle when its diameter is 
hnown, and conversely. 

If the diameter of a circle is a unit, its circumference will be 
3-141592653589793, &c. (§ 5). Denote this ratio by *, and put 

R = radius, 

D = diameter, 

C — circumference. 

Now since circumferences are to each other as their diame- 
ters, and consequently as their radii, we shall have 

C=Dx * = Dx 3-14159265, . . (1.) 
C=Rx2^Ex 6-28318531, . . (2.) 

D = Cxi=Cx 0-31830989, . . (3.) 

it 

E = Cxi = Cx 0-15915494. . . (4.) 

2* 

Using logarithms, we have 

log. = 0-4971499 + log. D, . . . (5.) 

log. C =-0-7981799+ log. R, . . . (6.) 

log. D = 1-5028501+ log. O, . . . (7.) 

log. E = 1-2018201 + log. O. . . . (8.) 

EXAMPLES. 

1. "What is the circumference of a circle whose diameter is 
12-5 feet ? Ans. 3-1416 x 12-5 = 39-27 feet, nearly. 

2. If the radius of the earth is 3956 miles, what is its circum- 
ference % Ans. 24856-281 miles, nearly. 

3. If the circumference of a circle is 100 feet, what is its di- 
ameter % Ans. 0-31830989 x 100 = 31*83 feet, nearly. 

4. If the circumference of a wheel is 15-5 feet, what is its 
radius % Ans. 2-4669 feet. 

5. "What is the circumference of a circle whose diameter is 
100 feet ? Ans. 314-159 feet. 



§54.] 



MENSURATION. 



69 



PROBLEM IX. 

To find the area of a circle when its diameter is known, and 
conversely. Also when the circumference is known. 

Denoting the area by A and continuing the notation as under 
Prob. VIIL, we have [Geom., B. V., Prop. XI.] 

A = \ of D x C. 

Substituting the value of C as already given, we have 



ie 



A = D 2 x - = D 2 x 0-78539816, . 
A = K 2 x * = E 2 x 3-14159265, . 
A = C 2 x i = C 2 x 0-07957747, . 

D = VAx 2V- = VAx 1-12837917, 

E = v/A x V-=VAx 0-56418958, 

C^v/AxV^^Ax 3-54490770. 

Using logarithms, we have 

log. A = 1-8950899 + 2 x log. D, 
log. A = 0-4971499 + 2 x log. E, 
log. A = 2-9007901 + 2 x log. C, 
log. D = 0-0524551 + \ x log. A, 
log. E = 1-7514251 + i x log. A, 
log. C = 0-5496049 + J x log. A. 



(1.) 
(2.) 
(3.) 

(5.) 
(6.) 



(8.) 

(9.) 

(10.) 

(11.) 

(12.) 



EXAMPLES. 

1. What is the area of a circle, whose diameter is 125 feet ? 

By equation (7), we have 

1-895090 
2 x log. 125 = 4-193820 

log. A = 4-088910 
A = 12271-8. 

If more decimals are required, they may be obtained by using 
equation (1), which gives 0-78539816x125x125=12271-84625. 



TO 



MENSURATION. 



[CHAP. V. 



2. "What is the number of square inches in a circular stand- 
top, whose radius is 15 inches? 

Ans. 3-1416 x 15 x 15 =706-86 sq. inches. 

3. "What is the area of a circular fish-pond, whose circumfer- 
ence is 25 rods ? 

Ans. 0-07957747 x 25 x 25 = 49'734 sq. rods. 

4. What is the number of rods in the diameter, the radius, 
and the circumference of a circle, which shall contain just 1 acre? 

Using equations (10), (11), and (L2), we have 



0-052455 
J of log. 160 = 1-102060 

1-154515 
D = 14-273. 



1-751425 

. . 1-102060 

0-853485 
E = 7-1365. 



0-549605 
. 1-102060 

1-651665 
C = 44-84. 



Note. — This last example would have required far more labor had we used 
equations (4), (5), and (6), which are independent of logarithms. 

5. How many chains must the diameter of a circular farm be 
which shall contain just 100 acres ? Ans. 35*68 chains. 



PROBLEM X. 

To determine formulas for the area and for the arc of a sector 
when the angle at the centre is known, and conversely. 

Denote the number of degrees which measures the angle at 
the centre by n, the length of the corresponding arc by c, and 
the area of corresponding sector by a. Then, since arcs of the. 
same circle are to each other as their corresponding angles at 
the centre ; also, since sectors are to each other in the same 
ratio, we shall have 

360 : n : : C :& 



360 : n : : A : a. 



And 



n 



C= 360 X °> 



n 



a 



360 



x A. 



(1.) 

(2.) 



EXAMPLES. 



1. What is the length of an arc of 15° of the earth, its entire 
circumference beins; 24856-28 miles ? 



Ans. ffo of 24856-28 



1035-68 miles, nearly. 



§54.] 



MENSURATION. 



71 



2. What is the area of a sector of 10 degrees of a circle, whose 
diameter is 10 feet ? 

If, in equation (2), we substitute the value of A as given by 
equation (1) of Prob. IX., it will become 

7i if if 

a = — - x - x D 2 = Mr x - x 100 = 218 so. feet, nearly. 

360 4 J60 4 * ' J 

3. What is the length of an arc of 1° of the moon, its diame- 
ter being 2160 miles ? 

In equation (1), substitute the value of C as given by (1) of 
Prob. VIII., and we have 

c = t^-— xif xD = 3I0 x * x 2160 = 18*849 miles, nearly. 
360 60 ' J 

4. An arc on the earth of 500 miles corresponds to how great 
an angle at the centre ? 



Equation (1) gives immediately [see equation (1), Prob. IX.] 

x 360° = r-242=7° 14' 31". 



o v _ n o 500 

^ = C X36 ° = 2485^28 



5. A sector whose area is 10 square feet corresponds to how 
great an angle at the centre, provided the diameter of the circle 
is 10 feet ? 

Equation (1) gives immediately [see equation (1), Prob. IX.] 

n = %- x 360° = iL x - x 360° = M, x - x 360° = 45°-8366 = 
A D 2 * * 

45° 50' 12". 

PROBLEM XL 



To find the avrea .of a segment of a 
circle. 

If n denote the number of degrees in 
the angle BAC, we shall have [Prob. 
X.] 



area of sector ABFC = 



n 

360 



x R 2 x «r. 




since A = R 2 x ^ , by equation (5), Prob. IX., 

area of triangle ABC = J R 2 x sin. n. 
[Prob. in., Second Rule.] 



72 MENSURATION. [CHAP. V. 

Hence the area of the segment BHCF, being the difference 
between the sector and triangle, is 

x it— i sin. n\ x E 2 . . . (1.) 



,360 

And the area of the segment BHCG, which is greater than a 
semicircle, is the sum of the sector CBG and triangle ABC. 
Hence, to determine the area of a segment, we have this 

RULE. 

Find the area of a sector which has the same arc as the seg- 
ment • also, the area of the triangle formed by the chord of the 
segment and the radii of the sector. 

Then take the sum of these areas when the segment exceeds the 
semicircle, and their difference tohen it is less. 

EXAMPLES. 

1. In a circle whose radius is 10 feet, find the area of a seg- 
ment whose arc corresponds with an angle of 10° at the centre. 

n 
Area of sector =— - x «r x E 2 = 4-A x 3-14159 x 10 2 = 8'727. 
360 ° 

" " triangle =| sin. 10° x 10 2 = i of 0-17365 xl0 2 = 8*683. 

The difference = area of segment = 0*044 of a sq. foot. 

2. In a circle whose radius is 15 rods, it is required to find 

the area of a segment whose arc corresponds to a central angle 

of 200°. 

Area of sector = 392-699 

" of triangle = 38-477 

" of segment 431-176 sq. rods. 

PROBLEM XII. 

To find the area of an ellipse. 

A line drawn through the centre of 
an ellipse is called its diameter. The 
longest diameter is called the trans- 
verse diameter ; the shortest is called 
the conjugate diameter. Thus AB is 
the transverse diameter, and CD is 
the conjugate diameter. These diameters mutually bisect each 
other at right angles. 




§ 55.] MENSURATION. 73 

The area of an ellipse may be found by this 

RULE. 

Multiply the product of the transverse and conjugate diame- 
ters fty 07854: = \ <k. 

A demonstration of this rule cannot be given by the element- 
ary principles of Geometry. 

EXAMPLES. 

1. How many square feet in the surface of an elliptical pond, 
whose transverse diameter is 100 feet, and conjugate diameter 
60 feet % Ans. 100 x 60 x 0'7854 = 4712*4 square feet. 

2. How many square inches is an elliptical table, whose trans- 
verse diameter is 5 feet 3 inches, and conjugate diameter 3 feet 
6 inches % And how many square feet ? 

a ( 2078-1684 square inches. 
14-4317 square feet. 



CHAPTEE VI. 



MENSURATION OF SOLIDS 



Which includes the measure of their surfaces as well as that of their 

volumes. 

§55. The common unit for measuring solids is a cube ; as, 
a cubic inch, a cubic foot, a cubic yard, &c. The values of the 
usual units of solid measure are given in the following 





TABLE. 


1728 


cubic inches == 1 cubic foot. 


27 


cubic feet = 1 cubic yard. 


4492| 


cubic feet = 1 cubic rod. 


128 


cubic feet = 1 cord of wood. 


231 


cubic inches = 1 gallon (liquid measure). 


268| 


cubic inches = 1 gallon (dry measure). 


2150| 


cubic inches = 1 bushel. 



74 MENSURATION. [CHAP. VI. 

§ 56. By an act of Parliament of Great Britain, which took 
effect on the 1st of January, 1826, the Imperial gallon of 277*274 
cubic inches was adopted as the only gallon. This value was 
found to be the measure of 10 pounds, avoirdupois, of distilled 
water. Estimating 8 gallons to the bushel, we have for the 
Imperial bushel 2218*192 cubic inches. 

New York as well as the other States of the Union still con- 
tinue to use the old English gallons as given in the foregoing 
table. 

PROBLEM I. 

To find the surface of a right prism, or of a right cylinder. 

RULE. 

Multiply the perimeter of the base by the altitude, for the con- 
vex surface. To which add the areas of the two bases if the 
entire surface is required. [See Geom., B. VIII., Prop. II. 
and III.] 

EXAMPLES. 

1. What is the entire surface of an octagonal prism, whose 
height is 25 feet, and each side of its base being 1 foot 3 inches ? 

1*25 x 8 x 25 = convex surface 250 sq. feet. 

area of bases 7*544 



257*544 sq. feet 

2. "What is the convex surface of a cylinder, whose length is 
40 feet, and its diameter 2 feet ? Ans. 251*328 sq. feet. 

PROBLEM II. 

To find the volume of a right prism, or of a right cylinder. 

RULE. 

Multiply the area of the base by the altitude. [See Geom., 
B. VII., Prop. XL, and B. VIII., Prop. I.] 

EXAMPLES. 

1. "What is the volume of a triangular prism, whose height is 
20 feet, and each side of whose base is 2 feet ? 

Ans. 34*641 cubic feet. 



§ 56.] MESTSUKATION. 75 

2. How many Imperial gallons in a cylindrical oil-can, the di- 
ameter being 20 inches, and depth 40 inches ? 

Denoting the diameter, in inches, by cZ, and height by A, and 
putting g for the number of inches in a gallon, we have 

Number of gallons = -— x d 2 x h. . . (1.) 

° kg v ' 

For Imperial gallons, g = 277*274 ; for United States, or old 
English gallons, g = 231. Hence 

Imperial gallons = 0-0028326 x d 2 x A, (2.) 

United States gallons == 0-0034 x d 2 x h. (3.) 

USING LOGARITHMS. 

log. [Imp. galls.] == 3-4521808 + 2 x log. d + log. k, (4.) 
log. [U. S. galls.] = 3-5314779 + 2 x log. d + log. h. (5.) 

Now, by equation (2), we find 

Arts. 0-0028326 x 20 2 x 40 = 45-32 Imp. gallons. 

3. How many cubic feet in a cylindric log 14 feet long, and 
14 inches in diameter ? Am. 14*966 cubic feet. 

4. How many cubic inches in a cylindric measure of 18J 
inches diameter, and 8 inches deep ? 

Am. 2150-425 cubic inches. 

Note. — The dimensions of the measure as given in the last example are those of 
the old English bushel, usually called the Winchester bushel ; so named from the 
place where it was deposited for safe keeping. 

5. How many United States gallons of oil in a can of 18 
inches diameter, the oil being only 13 inches deep ? 

Am. 14-32 U. S. gallons. 

PROBLEM III. 

To find the surface of a regular pyramid, or of a cone. 

RULE. 

Multiply the perimeter of the base by half the slant height. 
Add the surface of base when the entire surface is required. 

[See Geom., B. YIH., Prop. VI., where the demonstration for 
the cone is given. The rule is obviously correct in the case of a 
regular pyramid.] 



76 MENSURATION. [CHAP. VI. 

EXAMPLES. 

1. What is the convex surface of a cone whose slant height 
is 20 feet, and the diameter of the base 6 inches ? 

Ans. 15-708 sq. feet 

2. "What is the convex surface of an octagonal pyramid, its 
base being 10 inches on each side, and the slant height being 35 
feet % Ans. 116| sq. feet. 

PROBLEM IV. 

To find the volume of a regular pyramid, or of a cone. 

* 
RULE. 

Multiply the area of the base by one-third of the perpendicu- 
lar altitude. [See Geom., B. YIL, Prop. XYIL, and B. VILL, 
Prop. V.] 

EXAMPLES. 

1. How many cubic feet in a conical stick of timber 40 feet 
long, and 20 inches diameter at the base ? 

Ans. 29-0888 cubic feet. 

2. How many cubic yards in a conical stack of hay, which is 
18 feet in diameter and 27 feet high ? 

Ans. 84*823 cubic yards. 

3. How many cubic feet in a regular octagonal pyramid of 
marble, whose height is 30 feet, and a side of the base 2 feet ? 

Ans. 193*136 cubic feet. 

PROBLEM V. 

To find the surface of a frustum of a regular pyramid, or of 
a frustum of a cone. 

RULE. 

Multiply half the sum of the perimeters of the two bases by 
the slant height. When the entire surface is required, add the 
areas of the two bases. 

[See Geom., B. YIIL, Prop. YIL, which gives the demon- 
stration for conic frustum. The case of the pyramidal frustum 
is obviously the same.] 



§ 56.] MENSURATION. 77 

EXAMPLES. 

1. What is the entire surface of a frustum of a cone, the slant 
height of which is 15 feet, and the diameter of one base 2 feet 
6 inches, and that of the other 1 foot 3 inches ? 

Ans. 944934 sq. feet. 

2. What is the convex surface of a frustum of a regular hex- 
agonal pyramid, the slant height being 12 feet, each side of the 
larger base being 4 feet, and each side of the smaller base 3 feet ? 

Ans. 252 sq. feet. 

PEOBLEM VI 

To find the volume of a frustum of a regular pyramid, or of 
a cone. 

Let the area of the larger base of the frustum be denoted by 
A, and the area of the smaller base by a ; also let h denote the 
altitude. 

A frustum of a pyramid or cone is the difference between two 
entire similar pyramids or cones, the larger of which has A for 
the area of its base, and an altitude which we will denote by x. 
The smaller pyramid or cone will have a for its base and x—h 
for its altitude. 

Since the areas of the bases of similar pyramids or cones are 
to each other as the squares of their altitudes, we have 

A : a : : $ : (x—h) 2 ; 

extracting the square root of each term, we obtain 

l i 

A 2 : a 2 : : x ; x—h. 

This proportion immediately gives 

i i 

A 2 7 a 2 

x = — x fi ; x— fi = — j- x h. 

A 2 -«2 A 2 — a 2 

The volume of the first pyramid or cone is, by Prob. IY., 

3 

A 2 

jOl X g- X — - ^ T X jr lb. 

A 2 — a 2 



78 MENSURATION. [CHAP. VI. 

The volume of the second pyramid or cone is 



3 

a 2 



& x J (%—h) = — j J x J A. 

A 2 -a 2 

Their difference, which is the volume of the frustum, being 
represented by Y, becomes 

XL 3 

A 2 -a 2 
Hence the following 

RULE. 

Add together the areas of the tivo bases, and a mean propor- 
tional between them, and multiply this sum by one-third of the 
altitude. 

In the case of the cone, if D and d denote the diameters of 
the bases, we shall have 

if if i i if 

A = D 2 x T ; a == d 2 x -, and A 2 a 2 = ~Dd x -. 

4' 4' 4 

And V = (D 2 + d 2 + Bd) xhx 0-26179939. . (1.) 

If D, r7, and h are estimated in inches, we shall have the num- 
ber of United States gallons, which is the same as the number 
of old English gallons, in this volume, by dividing by 231. If 
we divide by 277*274, we shall obtain the number of Imperial 
gallons. Thus, 

U. S. gallons = (D 2 + d 2 + Dd) xhx 0-001 1333, (2.) 
Imp. gallons = (D 2 + d 2 + Dd) xhx 0*0009442. (3.) 

Using logarithms, we have 

log. [U. S. galls.] = 3-0543566 + log. (D 2 + d 2 + Di)+log. h, (4.) 
log. [Imp. galls.]=4-975059'5 + log. (D 2 + d 2 + Dd)+log. h. (5.) 

EXAMPLES. 

1. A block of marble is in the form of a frustum of a square 
pyramid : the larger base is 4 feet each way, and the smaller 
base is 3 feet on a side ; the height is 6 feet. How many cubic 
feet does it contain ? 

A = 4 2 = 16 ; a = 3 2 = 9 ; and A^ a* = 12. 
V = ( A + a + A* J) x J h = (16 + 9 + 12) x 2 = 74 cubic ft 



;c.] 



MENSURATION. 



79 



2. A cistern in form of a frustum of a cone is 9 feet deep, 
having for diameters 8 feet and 10 feet. How many U. S. gal- 
lons of 231 cubic inches will it contain ? 

Using equation (4), we have 

D 2 + d 2 + T>d = 35136 ; h = 108. 

3-054:357 
log. 35136 = 4-545752 
loar. 108 = 2-033424 



log. [IT. S. galls.] = 3-633533 Ans. 4300-6 U. S. galls. 

3. How many Imperial gallons in a cistern in the form of a 
frustum of a cone, the bottom diameter being 12 feet and top 
diameter being 10 feet, the depth also 10 feet ? 

Using equation (5), we have 

D 2 + d 2 + Vd = 52416 ; h = 120. 

4-975060 
log. 52416 = 4-719464 
log. 120 = 2-079181 



log. [Imp. galls.] = 3-773705 Ans. 5938'9 Imp. galls. 

4. How many cubic feet in a block of marble in the form of 

the frustum of a regular hexagonal pyramid, each side of the 

larger base being 4 feet, and each side of the smaller base being 

3 feet, and the altitude being 9 feet ? 

Ans. 288-386 cubic feet. 



PROBLEM VII. 

To find the volume, of a wedge. 

Definition. — A wedge is a solid 
bounded by five planes ; a rect- 
angle ABCD, called the base 
of the wedge ; two trapezoids 
ABEF, DCEF, called the sides 
of the wedge, and which intersect 
in the line EF, parallel to the base, 
which is called the edge of the 
wedge; and two triangles ADF, BCE, which are called 
ends of the wedge. If through E we pass the plane EMN 




the 
par- 



80 MENSURATION. [CHAP. VI 

allel to the end FAD, the portion EMBCJST thus cut off is a 
pyramid, and the remaining wedge having AMND for its base 
is evidently a triangular prism, and has for its measure one- 
half of a parallelopipedon, having the same base and same 
altitude. 

Hence if L = AB, the length of base, I = EF, the length of 
the edge, b = AD, the breadth of base, and h = EK, the alti- 
tude, then we shall have 

Volume of the wedge whose base is AMM) 

= J of AM x AD x EK = J Tbh. . . (1.) 

Volume of pyramid EMBCN = £ of MB x BC x EK - 

= i(L-l)hh=±LM-ilb7i. . . . (2.) 

Taking the sum, we have for the volume of the entire wedge 
iUh + iM = I (21, + l)bh. . . (3.) 

If the length of the wedge is less than the length of the edge, 
the volume sought will be the difference between the prism and 
pyramid. And in this case the volume of the pyramid will be 
J (I— L) bh = J Ibh—^ L£A, which subtracted from -j Ibh, the 
volume of the prism, we have 

llbh + ^Lbh = ±(2L + l)bh, . . (4.) 

which is precisely the same as expression (3). 
Hence the following 

RULE. 

To twice the length of the base add the edge, multiply the sum 
by the breadth of the base, and that product by \ of the height 
of the wedge. 

EXAMPLES. 

1. "What is the solidity of a wedge, whose base is 10 inches 
long, 4 inches wide, whose height is 8 inches, and whose edge 
is 9 inches ? Ans. 154| cubic inches. 

2. The length and breadth of the base of a wedge is 70 inches 
and 30 inches, the edge is 110 inches and the altitude 42 inches. 
What is the solidity? Ans. 30*3819 cubic feet. 



§56.] 



MEXStJEATION. 



81 




v PROBLEM VIIL 

To find the volume of a rectangular prismoid. 

Definition. — A rectangular pris- 
moid takes its name from its sem- 
blance to a prism. It may also be 
said to resemble a frustum of a 
quadrangular pyramid. The upper 
and lower bases are rectangles, 
having their corresponding sides 
parallel, and the convex surface 
consists of four trapezoids. The al- 
titude of the prismoid is the per- 
pendicular distance between the 
bases. 

Put L = AB, the length of lower base, 
B = AD, the breadth of " " 
I = EF, the length of upper base*. 
b = EH, the breadth of " " 
h = the altitude of the prismoid.. 

If we pass a plane through EF and DC, the prismoid will be 
divided into two wedges, whose bases are the bases of the pris- 
moid, and whose common altitude is the same as the altitude of 
the prismoid. 

The solidity of these wedges will be (Problem VII.) 

i (2 L + 1) BA, J (2 I + L) bh. 

Adding, we have for solidity of prismoid, 

i h(2BL + 2M + Bl + bL). . . . (1.) 

If we put p = \ (L + V) ; q = \ (B + 5), we shall have 

solidity of prismoid = \ h (BL -f bl + 4:pq). . (2.) 

In this last expression pq is the area of a parallel section 
equally distant from the two bases. Hence the following 

RULE. 

To the sum of the two bases add four times the area of a par- 
allel section equally distant from the bases, and multiply the 
sum by \ of the height. 

6 



82 



MENSURATION. 



[CHAP. VI. 



EXAMPLES. 

1. How many cubic feet in a block of marble in the form of 
a rectangular prismoid, the lower base being 4 feet by 3, the 
upper base 3 feet by 2, and the height being 5 feet? 

Ans. 441 cubic feet. 

2. How many cubic feet in a stick of 36 feet long, in the form 
of a rectangular prismoid, the one end being 20 inches by 16 
inches, and the other end being 14 inches by 12 inches ? 

Ans. 60 cubic feet. 

PROBLEM IX. 

To find the surface and solidity of a regidar polyedron. 

There are three regular bodies bounded by equilateral trian- 
gles : the Tetraedron, having 4 faces ; the Octaedron, having 
8 faces ; and the Icosaedron, having 20 faces. One, the Hex- 
aedron, is bounded by 6 equal squares ; one, the Dodecaedron, 
is bounded by 12 equilateral pentagons. 

If to these we add the sphere, which is a regular body, we 
shall have six for the total number of regular bodies which can 
exist. 

The following table shows the surfaces and volumes of the 
five polyedrons, having unity for the edges of each : 







TABLE. 


Names. 
Tetraedron 


No. of Faces. Surfaces. Volumes. 
. . 4 1-7320508 0-1178513 


Hexaedron 


. . 6< 


log. [0-2385607] log. [I '07 13344] 
6-0000000 1-0000000 


Octaedron 


. 8 


log. [0-77S1513] log. [0-0000000] 
3-4641016 0-4714045 


Dodecaedron 


. . 12 


log. [0-5395907] log. [1-6733937] 
20-6457288 7-6631189 


Icosaedron . 


. 20 


log. [1-3148302] log. [0-8844056] 
8-6602540 2'1816950 
log. [0-9375307] log. [0-3387940] 



The numbers included within the brackets are the logarithms 
of those numbers immediately above them. 



§ 56.] MENSURATION. 83 

Since surfaces of similar solids are to each other as the squares 
of their like dimensions, we may find the surface of any regular 
polyedron by this 

RULE. 

Multiply the square of one of the edges by the tabular surfa-m 
of the similar unit solid, as given in the foregoing table. 

Or using logarithms. 

To twice the logarithm of the edge add the tabular logarithm 
of the similar solid, as given in the table, and the sum will fo 
the logarithm of the surface. 

Again, since the volumes of similar solids are to each other 
as the cubes of their like dimensions, we may find the volume 
of any regular polyedron by this 

RULE. 

Multiply the cube of one of the edges by the tabular volume of 
the similar unit solid, as given in the table. 

Or using logarithms. 

To three times the logarithm of the edge add the tabular log- 
arithm of the similar solid, as given in the table, and the sum 
will be the logarithm of the volume. 

EXAMPLES. 

1. What is the surface and the volume of a regular icosae- 
dron, each edge of which is 10 inches ? 

j j Surface = 866*025 sq. inches. 
1 Volume = 2181*695 cubic inches. 

2. What is the surface and the volume of a regular dodecae- 
dron, each edge of which is 3 feet ? 

a ( Surface = 185-811 sq. feet. 
" \ Volume = 206-902 cubic feet. 

3. What is the surface and the volume of a regular tetrae- 
dron, each edge being 4 inches ? 

,, ( Surface == 27*712 sq. inches. 
Ans. < * . 

( Volume = 7*542 cubic inches. 



84: MENSURATION. [CHAP. VI. 

PROBLEM X. 

To find the surface of a sphere. 

RULE. 

Multiply the square of the diameter hy * = 3*1415926. [See 
Geom., B. Yin., Prop. IX.] 

EXAMPLES. 

1. Kequired the number of square inches in the surface of a 
ball 6 inches in diameter. Ans. 113*0976 sq. inches. 

2. How many square miles on the surface of the earth, it 
being 7912 miles in diameter ? Ans. 196662896. 

PROBLEM XL 

To find the volume of a sphere. 

RULE. 

Multiply the cube of the diamster hy \ cr = 0*5235988. [See 
Geom., B. VHL, Prop. XLLL, Scholium.] 

EXAMPLES. 

1. What is the volume of a sphere 6 inches in diameter ? 

Ans. 113*0976 cubic inches. 

2. How many cubic miles in the earth, its diameter being 
7912 miles ? Ans. 259332805350 cubic miles. 

§ 57. The following multipliers with their logarithms will be 
very convenient for reference. 

TABLE OF MULTIPLIERS. 

Log. of multipliers. 

1. Radius of a circle X6'28318531=Circuniference .....0-7981799 

2. Square of the radius of a circle X 3 141 59265= Area 0-4971499 

8. Diameter of a circle X3-14159265=Circumference 0-4971499 

4. Square of the diameter of a circle X0'78539816=Area .1-8950899 

6. Circumference of a circle X 01 59 15494=Radius .1 2018201 

6. Circumference of a circle X 03 1830989=Diameter 1-5028501 

7. Square root of area of a circle X 0-5641 8958=Radius .1-7514251 

6. Square root of area of a circle XM28379l7=Diameter 0*0524551 



§ 59.] SURVEYING. 85 

9. Radius of circle Xl-73205081=Side of inscribed equilateral triangle... 0-2385600 

10. Side of inscribed equilateral triangle X0'57735027=Radius of circle. . .1-7614394 

11. Radius of a circle Xl , 41421356=Side of inscribed square 0-1505150 

12. Side of inscribed square X0-707l0678=Ra«lius .1-8494850 

13. Square of radius of a sphere XI 2-5663706 l=3urface 1-0992099 

14. Cube of radius of a sphere X4-18879020=Volume 0-6220886 

15. Square of diameter of a sphere X3-14159265=Surface .04971499 

16. Cube of diameter of a sphere X0-52359878=Volume 1_-7189986 

17. Square of circumference of a sphere X0 31 830989=Surface 1^5028501 

18. Cube of circumference of a sphere X0-01688686=Volume 2 2275490 

19. Square root of surface of a sphere X0-28209479=Radius F4503951 

20. Square root of surface of a sphere X 05641 8958=Diameter 1-7514251 

21. Square root of surface of a sphere Xl'77245S85=Circumference 0-2485748 

22. Cube root of volume of a sphere X0-62035049=Radius T-7926371 

23. Cube root of volume of a sphere Xl'24070098=Diameter 0-0936671 

24. Cube root of volume of a sphere X3-89777707=Circumference 0*5908170 

25. Radius of a sphereXH5470054=3ide of inscribed cube 0-0624694 

26. Side of inscribed cubeX0-86602540=Radius .1-9375306 



CHAPTEK VH 

LAND SURVEYING. 
PRELIMINARY REMARKS, DESCRIPTION OF INSTRUMENTS, ETC. 

§ 58. The object of land surveying is to determine the di- 
mensions and areas of limited portions of the earth's surface. 
It also teaches the method of mapping, or delineating upon pa- 
per, the portions thus considered. 

On account of the spherical form of the earth, its surface is 
not plane, but curved. For such small portions as are usually 
surveyed for agricultural purposes, the curvature of this surface 
is disregarded, and the whole is considered as situated in the 
same plane ; but when larger portions, as towns, counties, &c, 
are to be surveyed, the spherical form of the earth is taken into 
account. 

§ 59. For the complete determination of a limited portion of 
a plane, it is necessary to know the length of each bounding line, 
and the angles which these lines make with each other. TVe 
will therefore proceed to describe the instruments used for meas- 
uring and planning, or mapping small surveys. 



86 SURVEYING. [CHAP. VIX* 

THE CHAIN. 

§60. We have (§53) already said that Gunter's chain is 
most commonly employed for measuring lines in a survey. 
The measures may, however, be made with any other conven- 
ient linear standard ; as a foot, yard, or rod. 

Instead of the chain,, surveyors sometimes employ a tape line, 
divided into links. It, is not, however, as accurate as the chain 
on account of its liability of stretching beyond its proper length. 
In measuring short distances, as in the case of city lots, the 
tape, divided into feet and inches, or into feet and tenths of a 
foot, is employed. 

§ 6 1. In Gunter's chain, the length of each link, together with 
half the rings connecting it with the adjoininglinks,is 7'92 inches. 
At every tenth link from each end of the chain is attached a 
piece of brass with one or more points ; that at the 10th link 
has one point, that at the 20th two points, that at the 30th three, 
that at the 40th four, the middle of the chain, or the 50th link, 
being marked with a large round piece of brass ; hence any dis- 
tance on the chain is readily counted. Part of the first link at 
each end is formed into a large ring for the purpose of holding 
it with the hand. 

The chain acquires extension by use ; it should, therefore, be 
frequently examined, and adjusted to the proper length by 
closing up some of the rings between the links ; for this pur- 
pose chains having three rings between the successive links are 
to be preferred to those having only two. 

THE OFFSET STAFF. 

§ 62. The offset staff is used to measure short distances, called 
onsets ; hence its name. It is usually ten links in length, the 
links being numbered 1, 2, 3, &c. It should be pointed with 
iron at one end, for the purpose of fixing it in the ground, as an 
object for ranging lines, for marking stations, &c. 

THE SURVEYOR'S CROSS. 

The cross is an instrument used by surveyors to locate lines 
perpendicular to each other. It is usually made of a round 
piece of hard wood, about 4 inches in diameter, with two fold- 



§63.] SURVEYING. 87 

ing sights at right angles to each other, or simply with two fine 
grooves sawed at right angles to each other, which answer the 
purpose of sights. It is sonietimes fixed on a staff of conve- 
nient length for use, which is shod with iron at the bottom, that 
it may be fixed firmly in the ground ; but in practice it is found 
more convenient to have a small pocket cross, which may be 
readily fitted to the offset staff. 

Directions for Measuring Lines on the Ground. 

§ 63. Besides the instruments already described, ten arrows, 
or iron pins, must be provided, about 12 inches long, pointed 
at one end so as to be readily pressed into the ground, the other 
end being formed into a ring to serve as a handle. When a 
line is to be measured, distinct marks are to be set up at the 
extremities of the line, and at intermediate points, when the 
extremities cannot be seen from one another on account of hills, 
woods, hedges, or other obstructions. Two persons, called chain- 
men, are then required to perform the measurement. The chain 
leader starts with ten arrows in his left hand, and one end of 
the chain in his right, while the follower remains at the first 
station point, who, looking at the staff or staves that mark the 
line to be measured, directs the leader to extend the chain in 
the direction of the staff or staves. The leader then puts down 
one of his arrows, and proceeds a second chain's length in the 
same direction, while the follower comes up to the arrow first 
put down. A second arrow being now put down by the leader, 
the first is taken up by the follower ; and the same operation is 
repeated till the leader has expended all his arrows. Ten chains, 
or 1000 links, having now been measured and noted in the field- 
book, the follower returns the ten arrows to the leader, and the 
same operation is repeated as often as necessary. When the 
leader arrives at the end of the line, the number of arrows in 
the follower's hand shows the number of chains measured since 
the last exchange of arrows noted in the field-book, and 
the number of links extending from the last arrow to 7000 
the mark or staff at the extremity of the line, being 600 

also added, gives the entire measurement of the line. 83 

Thus, if the arrows have been exchanged seven times, YfiaQ 
and if the follower have six arrows, and from the ar- 



88 SURVEYING. [CHAP. VII. 

row last put down to the end of the line be 83 links, the whole 
line will be 7683 links, or 76 chains 83 links, or, as usually writ- 
ten, 76*83 chains, the links being decimals of a chain. 

In using the chain, care must be taken to stretch it always 
with the same tension, as it will extend by much use, and will 
therefore require to be examined occasionally, and shortened, if 
necessary (§ 61). 

§64. As it is always the horizontal distances which are re- 
quired to be measured, great care should be taken to keep the 
chain, when stretched, in a horizontal position. In ascending a 
hill, it will be necessary for the hind chain-man to raise his end 
of the chain ; but in descending, the forward chain-man must ele- 
vate his end of the chain. In practice, it will be found more 
convenient to measure down a hill rather than up it, as the hind 
chain-man can then hold his end of the chain firmly to the pin 
in the ground, while the forward chain-man stretches the chain. 
The point on the ground directly under the elevated end of the 
chain may be determined by means of a plummet. When the 
surface is very much inclined, it will be necessary to measure 
only the distance of a part of the chain at a time. 

When a survey is made for a finished plan, all remarkable 
objects should be noted down ; as buildings, roads, rivers, ponds, 
foot-paths, gates, &c. 

§65. Instruments for laying down or plotting Surveys. 

COMMON DRAWING COMPASSES, OR DIVIDERS. 




The dividers consists of two legs, AB, AC, movable about a 
joint at A, so that the extremities B and C may be brought to 
any desired distance from each other within the limits of its 
span. It is employed to transfer and measure distances, and 
to describe arcs of a circle. 



§65.] 



SURVEYING. 



89 



PARALLEL RULE. 



This instrument con- 
sists of two equal and 
parallel rules, usually 
made of wood or ivo- 
ry, connected together 
with two equal cross- 
bars, as shown in the 
figure. It is used in drawing lines parallel to a given line. 



© o q 

'. \ — 

O o Q 



B 8- 6-4-2 A 

!■ i ' ' i m I ' 



SCALE OF EQUAL PARTS. 
2 3 4 5 



A scale of equal parts is formed by dividing a line into equal 
portions. One of the equal portions, as AB, may be subdivided 
into ten equal parts, which, will allow of our taking units and 
tenths from the scale. 



DIAGONAL SCALE OF EQUAL PARTS. 



A-2-4-6-8B 



1 


1 ! ! 




u 


{ 


1 




M 


1 


i 1 




111m 








11 


i 




i 




Mil llllll! 


/ 




[ 




i 1 


I 




1 






1 1 ■Hull 


I 




l 






1 1 PI 










IMP 


l i 






lii 



•02 
i -04 

06 

03 



DF 



U 



In this scale, the whole width is divided into ten equal and 
parallel strips, and one of the equal units of length, as AB, is 
also divided into ten equal parts ; but the lines forming these 
divisions pass diagonally across the width of the scale, so as to 
gain one division in passing across the whole width. Since 
each diagonal line is one-tenth further from the line AD at its 
lower extremity than it is at the upper extremity, it follows that- 
each tenth is in effect divided into ten equal portions, so that 
the unit is divided into hundredths. 



SEMICIRCULAR PROTRACTOR. 



This instrument is used to measure given angles, also to de- 
termine how to draw lines which shall form with each other any 



90 



SURVEYING. 



[CHAP. VII. 



desired angle. This instrument is sometimes made of a piece 
of thin transparent horn, instead of metal : the lines of the paper, 
although covered by the protractor, are in this case visible, on 
account of the transparency of the horn. 




The above comprise the most essential instruments used in 
plotting fields ; there are, however, a great many other instru- 
ments which have been devised which at times are very conve- 
nient. Their use will be readily understood when seen. 

§ 66. INSTRUMENTS FOR MEASURING ANGLES. 



THE SURVEYOR S COMPASS. 



This instrument makes known the north and south direction, 
by means of a magnetic needle, which is so balanced in a hori- 
zontal plane as to allow it freely to assume the magnetic merid- 
ian, which usually does not differ much from the true meridian. 
The compass-lox, in which the needle is adjusted, is in the form 
of a circle ; the diameter is usually about 8 or 10 inches. The 
circumference is divided into degrees, and sometimes into half 
degrees, and the degrees are numbered from a fixed diameter 
in both directions from 0° to 90°. The sights, which are perpen- 
dicular to the plane of the graduated circle, are provided with 
a wide and narrow aperture for the greater convenience of ob- 
servation. This instrument is usually supported by a single 
staff, shod at the bottom with iron, to allow of its being firmly 
fixed in the ground. Sometimes it is supported by means of a 
tripod, which is preferable, especially in surveying land which 
is very stony. 



67.] 



SURVEYING. 



91 



Usually two spirit-levels are placed at right angles with, each 
other in the plane of the graduated circle. By means of these 
levels we are enabled to place the plane of the compass -box in 
a horizontal position. 



THE THEODOLITE. 



This instrument is quite complicated in its construction, a 
full description of which would take up more space than can 
well be spared in this elementary work. We will, however, re- 
mark, that it is adapted for the measurement of vertical angles, 
as well as those which are horizontal. 

In Practical Astronomy, a great variety of instruments for 
measuring angles have been constructed ; but in Land Survey- 
ing, the Compass and Theodolite are the instruments most com- 
monly used for this purpose. 



CHAPTEE YIII. 



Calculation of Areas Trigonometrically by Dividing the Field 

into Triangles. 



§67. Surveys with the Chain only. 

Measure the sides of the field, 
and a sufficient number of di- 
agonals, to divide the whole 
into triangles. 

Thus, suppose we find by 
measurement AB=5*63 chains ; 
BC = 5-llcA.; CD = 6-10 eh. ; 
DE = 5-93 ch. ; EA = 6'53 ch. : 




DA = 6-02 ch. ; DB = 6'97 ch. 



Proceeding as in Prob. F., Chap. FZ, we have 



92 



SURVEYING. 



[chat. vm. 



Triangle ABE. 

EA = 6-53 
DA= 602 
DE = 5-93 



2 ) 18-48 



\ 



9-24, log. 
2-71, log. 
3-22, log. 
3-31, log. 



0-965672 
0-432969 

0-507856 
0-519828 



Leter = 


18-48 2" 


) 2-426325 


log. area = 


: 1-213162 


16-337 = 


= area ADE 


Triangle ABB. 




DB = 6-97 




DA- 6-02 




AB - 

2) 


5-63 




18-62 






f 9-31, log.- 


: 0-968950 


< 


2-34, log. = 


■ 0-369216 


3-29, log. = 


0-517196 




,3-68, log. = 


0-565848 



Perimeter = 18-62 2 ) 2-421210 

log. area = 1*210605 
16-241 = area ABD. 



Triangle BCB. 

DB= 6-97 
CD- 6-10 
BC = 5-11 



2)18-18 



• 



f 9-09, log. = 0-958564 
2-12, log. - 0-326336 
2-99, log. = 0-475671 
3-98, log. = 0-599883 



Perimeter = 18-18 2 ) 2-360454 
log. area = 1-180227 



§ 67.] 



SURVEYING. 



93 



15-144 = area BCD, 
16-241= " ABD, 
16-337= " ADE, 




47*722 = " ABODE in sq. chains, 
or, 4*7722 in acres and decimals, which equals 4JL SB. 3JP. 

2. Find the area of a field 
whose sides and diagonals are as 
follows : 

AB=4-17 ch.; BC = 11-93 
ch. ; CD = 8-16 ch. ; DE = 4-01 
ch. ; EA = 4-97 ch. ; EB = 3-98 
ch. ; EC = 10-02 ch. 

Arts. 4 A. IB. 1\P. 

3. Find the area of 
a field whose sides and 
diagonals are as fol- 
lows: 

AB=10-31 ch. ; BC 
=15-15 cA.;CD=9-99 
ch. ; DE = 7-50 ch. ; 
EF=17-16cA.; FA = 
10-01 ch.] AE =18-27 
ch.; BE = 17-88 ch.; 
BD =16-46 ch. 

4. Find the area of a 
field whose sides and di- 
agonals are as follows : 

AB=15-30 ch. ; BC=14 
ch.; CD=6-75cA. ; DE= 
8-10 ch. ; EF = 11-20 ch. ; 
FA=10-20cA. ;BD=12-10 
ch. ; BE=17-50 ch. ; BF= 
22-50 ch. Ans. 24.4. 2B. 12P. 

5. In the following field, after measuring the sides, a point N, 
from which all the corners could be seen, was assumed, and the 
distances to the respective corners were measured. Find the 
area, on the supposition that these lines are as follows : 




Ans. 30.4. SB. 35JP. 




94 



SURVEYING. 



[chap. vni. 



CD = 4-04 ch. ; DF = Y'25 ch. ; FG = 3-87dL; GH=4-39 
ch. ; IIL = 5-39 ch. ; LM = 3*56 ch. ; MC «= 11-13 ch. ; NC = 



3-74 cA. ; JSTD = 4-81 
NH = 8-76 ch. ; NL = 



ch.\ NF-8-20 eh.\ NG = 9-18 ch.; 
8-68 ch. ; NM = 8*26 cA. 

^4tw. 1(L4. 3P. 6fP. 




68. Surveys made with the Chain and Compass. 



-A : 



The bearing of a line, taken 
with a compass, is the angle 

which the line makes with the ^ •-. ..B 

meridian. If the angle BAN, **>•- 

which the line AB makes with "w 

the meridian NS, is 63°, the 

bearing of AB is north 63° east. 

The reverse bearing of this line 

is south 63° west. The bearings l> 

are always estimated from the 

north or south points around towards the east or west. Thus, 

AC is north to the west, AD is south to the west, and AF is 

south to the east. 

In ordinary cases, the bearings of lines in a survey are not 
given with an accuracy beyond what can be expressed in quar- 
ters of degrees. 



E 



70.] 



SURVEYING. 



95 



§ 69. The angle between two lines proceeding from the same 
point may be found, when their bearings are known, by the fol- 
lowing 

RULES. 

I. If both courses are north or south, and both east or west, 
take their difference. 

II. If both are north or south, the one east and the other west, 
take their sura. 

III. If one is north and the other south, and both east or west, 
take the supplement of their sum. 

IV. If one is north and the other south, and one east and the 
other west, take the supplement of their difference. 

The correctness of these rules is readily discovered by refer- 
ence to the preceding diagram. Indeed, it is about as well in all 
cases to make a rough sketch of the two lines and the meridian 
passing their angle of meeting, and then by inspection we shall 
readily see how we are to find their included angle. 

The above rules are derived on the supposition that the bear- 
ings are taken from the same point of meeting. When we wish 
the angle included between two sides of a field, whose bearings 
are given in the ordinary way, we must, before applying the 
above rules, reverse one of the bearings. 

§ 70. To plot a field which has been surveyed with a chain 
and compass. 

Suppose the bearings and dis- 
tances of the sides of a field to be 
as follows : 



AB 
BC 
CD 
DE 
EA 



N. 50t°«E. 
S. 41° E. 
S. 1\° E. 
S. 681-° W. 

H. 41° W. 



5-08 ch. 
4-18 ch. 
2-42 ch. 
3-96 ch. 
4-99 ch. 



Draw NS to represent a meridian 
passing through the first station or 
corner of the field. By means of 
the protractor find the direction of 
the line AB, so that the angle BAN" 




96 



SURVEYING. 



[chap. VHI. 



may bo 50}°, which is the bearing of the first side. Then by 
means of the scale of equal parts make AB equal to 5*08 ch., 
which is the length of the first side. Through B, by means of 
the parallel rule, draw a line parallel to JSTS, which will be a 
meridian passing through the second corner of the field. Draw 
BC, making an angle with this second meridian equal to 41°, and 
make BC equal to 4*18 ch. Proceed in the same way for the 
other sides of the field. If the survey was accurately made, and 
the plotting performed without error, the extremity of the last 
side EA will fall on A, the place of beginning. 

We might have determined the angles made by the adjacent 
sides of the field by the rules under § 69, and then we could 
have plotted the field without drawing meridians through each 
corner. 

Applying this method, we find ABC = 91*° ; BCD = 1461° 5 
CDE = 104i° ; DEA = 109^° ; EAB = 88|°. The sum of all 
these angles is 540° = 6 times 90°. (Geom., B. I., Prop. XXIV.) 

§71. Having plotted the above field, we will proceed to 

determine its area as follows : 

Draw the diagonals CA and CE, 
dividing the field into three trian- 
gles. 

In the triangle ABC, we have 
the two sides BA and BC, and by 
§ 69, we find their contained angle 
ABC to be 91}°. Hence we find 
its area by Second Rule, Prob. III., 
Chap. V., as follows : 

log. 5-08 = 0-705864 

log. 4-18= 0-621176 

sin. 91° 15' = 9-999897 




11-326937 
subtract, constant = 10*301030 



log. area= 1*025907 



Area = 10-6147 sq. ch. 



§ 71.] SURVEYING. 97 

By Theorem II, Chap. IV., we have 

ar. co. log. 9-26 = 9-033389 

log. 0-90 = 1-954243 

cot. 45° 37' 30" = 9-990524 



•J Sum = 
| Diff. = 


= 44° 22' 30" 

= 5° 25' 56" 


BCA = 
BAC = 


: 49° 48' 26' 
= 38° 56' 34" 



tang, of j diff. = 8-978156 



By Theorem I, Chap. IV., we have 

ar. co. sin. 38° 56' 34" = 0-201664 
sin. 91° 15' = 9-999897 
log. 4-18 = 0-621176 

log. AC = 0-822737 

By § 69, we find angle BAE = 88° 45'. Hence angle CAE = 
BAE-BAC = 88° 45' -38° 56' 34" = 49° 48' 26\ 

Now by Second Rule, Problem III, Chap. V., we find the 
area of triangle CAE as follows : 

log. AC = 0-822737 

log. AE (4-99) = 0-698101 
sin. 49° 48' 26" = 9-883023 



11-403861 
10-301030 



log. area = 1-102831 
Area = 12-6716. 

In triangle CDE, we find, § 69, the angle CDE = 104° 15' ; 
then, as above, we have 

log. DC (2-42) - 0-383815 
log. DE (3-96) = 0-597695 
sin. 104° 15' = 9-986427 



10-967937 
10-301030 



log. area = 0-666907 
Area = 4*6442. 

7 



98 



SURVEYING. 



[CHAP. VIII. 



Collecting, we have 



Area of triangle ABC 



u 



= 10-614? sq. ch. 
CAE = 12-6716 " 
CDE = 4-6442 " 



" " field ABCDE = 27*9305 " 

After finding the diagonals CA and CE, we might have com- 
puted the areas of these three triangles by the Third Rule, Prob. 
HI., Chap. Y. 

After a similar manner we might divide any field, which has 
been surveyed with the chain and compass in the usual way, 
into triangles, and then compute the area of each triangle, and 
taking their sum, thus obtain the area of the entire field. 

§ 72. Survey of a field from two stations within, from which 
all the corners can he seen. 



--AG 




Stationary line AB, !N" 

Bearings of Corners 
from Station A. 

AC = N. 45i° W. 
AD = N. 9J° E. 
AF = K 70i° E. 
AG = S. 84i° E. 
All = S. 56i° E. 
AL = S. 20i° E. 



771° E. 5 chains. 



AM = S. 



3i° W. 



Bearings of Corn/ 


rs 


from Station B. 




BC 


= N. 


7.81° 


w 


BD 


= N". 


48i° 


W 


BF 


= K 


591° 


E. 


BG 


= 6. 


65|° 


E. 


BII 


= S. 


22° 


E. 


BL 


= s. 


iij° 


W. 


BM 


= s. 


30° 


w. 



72.] 



sujavErixa. 



99 



"We will first consider the field as divided into seven triangles 
by lines drawn from the station A, to the different corners. By 
§ 69 we can find the angles included between any two lines 
whose bearings are given. There will be seven triangles formed 
having the stationary line AB for a base, and their vertices sit- 
uated at the respective corners of the field. Thus, ABC, ABD. 
ABF, &c. The triangle ABC gives (Theorem I., Chap. IV.) 

sin. ACB : sin. CBA : : AB : AC ; 
sin. 33° : sin. 24° : : AB : AC. 



Hence, 



sin 24:° 
AC = =-=L x AB. 



QQO 



Sill. 66 



Proceeding in this way, we find as follows : 



Length of Lines. 



Contained 


Angles. 


CAD = 


54f 


DAF = 


61° 


FAG = 


25i° 


GAH - 


28i° 


HAL = 


36° 


LAM = 


OO3 
Zo 4 


MAC = 


131° 


Sum = 


360° 



TrianorleABCffives AC = 



a 



tt 



u 



u 



u 



ABD 

ABF 

ABG 

ABH 

ABL 

ABM 



AD 



sin. 24° 
sin. 33 J 
sin. 541° 



sm. Oi-h 



7J_-> 
2 



xAB. 
x AB. 



AF= sin li 61| !x 

sm. 11° 
AG= ^W 

sm. iyi J 

sm. 341° 



cc 



AL = 
AM = 



sin. C6° 
sm. 31f J 
sin. 47^° 
sin. 26^ J 



x AB. 
x AB. 
xAB. 



We now know the sides and contained angles of the seven 
triangles having their vertices at A, and for bases the respective 
sides of the field. The areas of these triangles are given by 
Second Bale, Prob. Iff., Clia-p* V., as follows : 



LifC. 



100 



SURVEYING. 



[OHAP. VIII. 



CAD = 



The area of these triangles. 

sin. 24:° x sin. 54^° x sin. 54f 
sin. 33° x sin. 571° 



sq. chains. 



*. . _, sin. 54]-° x sin. 161f° x sin. 61' 
DAF = — 



FAG = 
GAH= 



sin. 57J° x sin. 11° 
s in. 161 1° x sin. 142 f° x sin. 25^ ° 

sin. 11° x sin. 19£° 

sin. 142j° x sin. 99|° x sin. 28^° 

sin. 191° x sin. 34i° 



TT . T sin. 991° x sin. 66° x sin. 36 c 
HAL = - 



sin. 31]-° x sin. 311° 



LAM 



sin. 66° x sin. 47|° x sin. 23| 
sin. 31|° x sin. 26^° 



30 



ftr . _ sin. 471° x sin. 24° x sin. 131 c 

MAC == — — 

sin. 26|° x sin. 33° 



x 



x 



x 



X 



X 



X 



2 
AB 2 

"2 

ab 3 

2 
AB 5 

2 
AB 2 

2 
AB 2 

2 
AB 2 

~2~ 



= 17-266 
•-= 16-067 
== 19-036 
= 22-353 
= 14-442 
= 11-641 



108-141 
The logarithmic computation of the areas of the above trian- 



gles is as follows : 



AB 2 _5 2 __ 

"2 2 - 125 * 



Log. 12-5 = 1-096910. 



Triangle CAD. 
log. 12-5 = 1-096910 
sin. 24° = 9-609319 
sin. 54|° = 9-909328 
sin. 54j° = 9-912031 
ar. co. sin. 33° = 0-263891 
ar. co. sin. 57|° = 0*073971 



log. area = 0-865444 
Area CAD = 7-3357. 



Triangle DAF. 

1-096910 

sin. 54^° = 9-909328 

sin. 161f° = 9-495772 

sin. 61° =9-941819 

ar. co. sin. 57| a = 0-073971 

ar. co. sin. 11° = 0-719401 



log. area = 1-237201 
Area DAF = 17-2663. 



Triangle FAG. 
log. 12-5 = 1-096910 
sin. 161 J° = 9-495772 
sin. 142|° = 9-781966 
sin. 25i° = 9-629989 
ar. co. sin. 11° = 0-719401 
ar. co. sin. 19J° = 0*481893 



log. area 



1-205931 
Area FAG = 16-0668. 



Triangle GAH. 

. 1-096910 
sin. 142 j° = 9-781966 
sin. 99}° = 9-994003 



sin. 
ar. co. sin. 
ar. co. sin. 



28|° = 9-675155 
19i° = 0-481893 
341° = 0-249642 



log. area =1-279569 
Area GAH = 19-0357. 



§72.] 



SURVEYING. 



101 



Triangle HAL. 

log. 12-5 =1-096910 
sin. 99J° = 9-994003 
sin. 66° = 9-960730 
sin. 36° = 9-769219 
ar. co. sin. 34^° = 0-249642 
ar. co. sin. 31| ° = 0-278838 



log. area = 1-349342 
Area HAL = 22-3533. 



Triangle LAM. 

. 1-096910 

sin. 66° =9-960730 

sin. 47|° = 9-867631 

sin. 23$ ° = 9-605032 

ar. co. sin. 31f° = 0-278838 

ar. co. sin. 261° = 0-350473 



log. area = 1-159614 
Area LAM = 14-4415. 



Triangle MA C. 
log. 12-5=1-096910 



Results collected. 



sin. 


471° 


= 9-867631 


sin. 


24° 


= 9-609313 


sin. 


131° 


= 9-877730 


ar. co. sin. 


261° 


= 0-350473 


ar. co. sin. 


33° 


= 0-263891 



log. area = 1-065998 
Area MAC = 11-6412. 



CAD 



7-3357 



DAF = 17-2663 
FAG = 16-0668 
GAH= 19-0357 



HAL = 
LAM = 



22-3533 
14-4415 



MAC= 11-6412 



108-1405 



Hence the area of the field is 108*141 sq. ch., nearly. 

Considering the field as divided into seven triangles by lines 
drawn from the station B, we have 



Contained Angles. 

CBD = 301° 
DBF = 107i° 
FBG = 55i° 
GBH= 43i° 
HBL= 331° 
LBM= 18i° 
MBC= 7U° 



Length of Lines. 



Sum = 360° 



"RO 


sin. 


123° 




sin. 


33° 


BD 


sin. 


68J° 


sin. 


571° 


BF 


sin. 


>-T\0 

* 4 


sin. 


11° 


BG 


sin 


.18° 


sin. 


191° 


BH 


sin. 


461° 




sin. 


341° 


BL 


sin. 


821° 




sin. 


31f 


BM 


sin. 


106° 


sin. 


26i° 



x AB. 
x AB. 
x AB. 
xAB. 
x AB. 
x AB. 
x AB. 



102 



SURVEYING. 



[chap. vni. 



CBD 



The area of these triangles. 

sin. 123° x sin. 68|- ° x sin. 30|-° 
sin. 33° x sin757|° 



X 



AB 2 



^t, sin. 68-J° x sin. 7}° x sin. 107^° * AB 2 
DBF = K — ... 4 . — — — x 



FBG = 



GBH- 



BGBL = 



LBM = 



MBC = 



sin. 57|° x sin. 11° 
sin. 1\° x sin. 18° x sin. 55^-° 

sin. 11° x sin. iy±° 
sin. 18° x sin. j6j° x sin. 43j-° 

sin. 19|° X sin. 34^° 

sin. 461° x sin. 82|° x sin. 33|-° 

sin. 34i° x sin. 31f° 

sin. 82^° x sin. 106° x sin. 181° 



x 



x 



X 



2: 

AB 2 

2 
AB 2 



2 
AB 2 



x 



2 
AB 2 



sg. chains. 

= 10-679 
= 8-683 
= 6-386 
= 10-303 
= 16-675 



sin. 31f° x sin. 26J° 2 

sin. 106° x sin. 123° x sin. 7U° AB 2 



= 16-090 



sin. 26i° x sin. 33° 



x 



2 



= 39-325 



108-141 
or, 10A. 3i?. 10iP. 



Tliis result agrees precisely with the first result, which ought 
to be the case if no error is made. 

§ 73. Survey of afield from two stations without, from which 
all the corners can be seen. 




§ 73.] SURVEYING. 103 

Stationary line AB, S. 88° 30', E. 19-20 chains. 

Bearings of Comers Bearings of Corners 

from Station A. from Station B. 

AC = N. 72° E. BC = K 201° E. 

AD = 1\. 39° E. BD=K 24° W. 

AE = 1ST. 91° E. BE - K 50° W. 

AF = JST. 16° E. BF - N. 29i° W. 

AG = K 141° E. BG = K 21J° W. 

AH = K 40° E. BH = K 5° E. 

Taking into account the triangles formed by the lines drawn 
from the station A to the different corners, we shall find the 
length of these lines as below : 

Contained Angles. Length of Lines. 

CAD ==33° AO=$^xiB. 



xAB. 



DAE=29f°~ sin. 51^° 

EAF = 6f° + _ sin. 64j° 

FAG = li°- sin. 63° 

GAH = 25i°+ _ sin. 38|° 

HAC = 32° + ^ "iS759p XA±J - 







Sum = 0° AF = ™l*|£ x AB. 

sin. 451° 

. _, sin. 67° . t, 
AG = . Q „ x AB. 
sin. 36 

A TT Sin. OO-o A t-v 

The areas of these triangles. S g chains 

= Bin. 109° x sin. 64i x sin. 33° AB 2 = ± ^ 

sin. 51i° x sin. 63° 2 

~ . _ sin. 641° x sin. 38^° x sin. 29f AB 2 

DAE = ?— — .^-^^T5 x -15- = 67-112— 

sin. 63° x sin. 59£° 2 

EAF _ sin. 381° x sin. 59j° x sin. 6 j° y AB 2 = lg . 990 + 
sin. 59}° x sin. 45^° 2 

_ . ^ sin. 59^° x sin. 67° x sin. U° AB 2 _ . , , 

F -^G = -• — r^i = — o*o — — x -77- = 9-144- 

sm. 451 x sin. 36° 2 

^ . _ sin. 67° x sin. 931° x sin. 25J° AB 2 M a OKO , 

GAH = : — — — 2 - — — Q *- x ——= 216-252 4- 

sm. 36° x sm. 3o° 2 

„ . ~ sin. 931° x sin. 109° x sin. 32° AB 2 ank OKa , 

HAC = -. — 7 r^ ; — ^q-^ x— —-=205-356 + 

sin. 35° x sin. 511° 2 

241-481 
or, 24JL 0B. 23-696P. 



104 SURVEYING. [CHAP. VIII. 

The triangle A CD may be conceived as generated by the rev- 
olution of the line AC about the point A, so varying in length 
as it revolves towards the left, as to describe by its extremity 
the straight line CD. To describe the second triangle DAE, it 
continues to revolve towards the left ; but in describing the third 
triangle EAF, the revolution is towards the right. The fourth 
triangle requires the revolution of the line towards the left, while 
the fifth and sixth are in succession described by the revolution 
towards the right. ]STow, those triangles generated by the revo- 
lution of this variable line towards the right I have considered 
as positive, and have marked them with the + sign, while those 
formed by the opposite revolution I consider as negative, and 
have marked them with the — sign. The algebraic sum being- 
taken, we obtain the area of the field. 

The contained angles I have also considered as — or +, ac- 
cording as they were passed over by a revolution towards the 
left, or contrariwise, by a revolution towards the right. Their 
algebraic sum is 0°, as it evidently ought to be, since the varia- 
ble line has returned to its original position after describing the 
last triangle. 

If we now take into account the triangles formed by the lines 
drawn from the station B to the different corners, we shall have, 
in a similar manner, as follows : 

Contained Angles. Length of Lines. 

OBD=44*'- EC = Sin - ] d X x AB. 

DBE =26° - sin. 51J- 

EBF = 20*° + sin. 62J° B 

GBH=26|° + sin. 82J° A „ 

HBC=15J° + BE =shr^F xAR 

Snm=0° ffl^^ 

sm. 45^° 

_, ~ sin. 77° . -p, 
BG= . x AB. 

sm. 36 

BH = sjn. 51 jf xAR 

sin. 35 



§74] 



SURVEYING. 



105 



CBD 

DBE 

EBF 

FBG 

GBH 

HBC 



The areas of these triangles. 

sin. 52i° x sin. 19*° x sin. 44i° AB 2 



sin. 63° x sin. 51£° 
sin. 82} x sin. 52 \° x s in. 26 c 



- x 



sin. 591° x sin. 63° 

_ sin. 75^° x sin. 82^° x sin. 20 
"" sin. 45i° x sin. 59i° 

_ sin. 77° x sin. 75J° x sin. 7f ° 
~~ sin. 36° x sin. 45^° 

_ sin. 511° x sin . 77° x sin. 26^° 
sin. 35° x sin. 36° 

_sin. 51^° x sin. 19j° x sin. 15^° 
sin. 514° X sin. 35°~ 



x 



- X 



X 



X 



X 



2 

AB 3 

2 

AB 2 

2 
AB 2 

~2~ 

AB 2 



sg. chains. 

= 49-065. 



2 
AB 2 



2 



= 82-950- 
= 102-640 + 
= 56-170 + 
= 186-019 + 
= 28-667 + 



241-481 



The same rule in regard to the plus and minus areas is here 
observed as in the first method. 

The agreement of the two methods is good evidence in favor 
of their accuracy. 

§ 7 4. Examples for Practice. 



1. From the following field- 
notes compute the area of the 
field whose plot is here an- 
nexed : 



FA=K 


48J° "W. 


5*51 chains. 


FB=K 


59J° E. 


3-31 " 


FC=S. 


65J° E. 


4-69 " 


FD=S. 


22° E. 


6-42 " 


FE=S. 


771° W. 


5-00 " 



Arts. 5A. 0B. 38-67P. 




106 



SURVEYING. 



[chap. VIII. 



2. Compute the area of 
the adjacent field, having 
given as follows : 

FA=S. 77J° W. 
FB=S. 65i°E. 
FC=S. 22° E. 
FD=S. lli° W. 
FE=S. 30° W. 10-77 " 
Am. 5A. 2fi. U\P. 



5-00 clis. 
4*69 " 
6-42 
9-42 " 



3. Plot and com- 
pute the area of the 
field, whose field- 
notes obtained in the 
usual way are as fol- 
lows : 

N.38}°E. 3-04 v c7i. 
S. 72i° E. 2-41 " * 
S. 22f° E. 2-52 " 
S. 83i° W. 2-97 " 
1ST. 65f ° W. 2-42 « 




AnsAA. 0B. 14JP. 



4. Plot and compute the area of the field, which, surveyed in 
the usual way, give the following : 




§71.] 



SURVEYING. 



107 



K 60J° E. 2-17 chains. 

K 79° E. 4-61 

S. 70|°E. 2-00 

S. 30|° W. 6-05 

K 66° W. 4-59 

K 26J° W. 2-30 



u 



a 



.4nfc 2,4. SB. 16JP. 



5. Compute the area of a field which, surveyed from two sta- 
tions from without, give the following : 

Stationary line AB, ]ST. 73° E. 6 chains. * 




Bearings of Corners from A. 

AC = K 10i° W. 



AD 



K 161° E. 



AE = K 30i° E. 
AF = K 46f ° E. 
AG = 1ST. 62i° E. 
AH = K 1J°W. 



Bearings of Corners from B. 

BC=K 57° W. 
BD=K13J° "W. 

BE - K 6£° E. 
BF = 1ST. 26J ° E. 
BG = K 41±° W. 
BH = K71i° "W". 
Ana. 6A. IB. 0}P. 



108 



SURVEYING. 



[chap. vni. 

6. Find the area of the adjacent field, having given as follows : 
Stationary line AB, 1ST. 14° E., 20 chains. 




E 



Bearings of the Corners from 
Station A. 



AC 
AD 
AE 
AF 
AG 
AH 



1ST. 38i° E. 



S. 69° 
S. 59° 
K 63° 
K 21° 
North. 



E. 

W. 

"W. 

w. 



Bearings of the Corners from 
Station B. 



BC 
BD 
BE 
BF 
BG 
BH 



. S. 82° E. 

. S. 17° E. 

. S. 28° W. 

. S. 49° W. 

. K 76° W. 

. N. 24° W. 
Ana. 69A. 17?. 1-4T2P. 



§75.] 



SURVEYING. 



109 



CHAPTER IX. 

RECTANGULAR METHOD OF COMPUTING AREAS. 

§ 75. Suppose we are required to determine the area of the 
field ABCDFGA. We take the bearings of the several sides 
by means of the compass, and measure their lengths with the 
chain. 




Through the first station A draw the meridian !N"S, and the 
east and west line EW. Then from the several corners of the 
field draw perpendiculars to these two lines, which perpendicu- 
lars we have represented bj dotted lines. 

Prepare a table, as below, of eleven columns. In the first 
column register the numbers denoting the sides. In the second 
column place the bearings of the several sides as determined in 
the field, by means of the compass. In the third column place 
the lengths of those sides, as measured with the chain. 



no 



SURVEYING. 



[CHAP. IX. 



Tli en with the bearings and distances of the respective sides 
take from Table IV., the Traverse Table, their latitudes and de- 
partures, which must be placed in the 4th, 5th, 6th, and 7th 
columns. The North latitudes being written in column !N", and 
the South latitudes in column S. The East departures are to be 
written in column E, and the West departures in column W. 



Nos. 


Bearings. 


Dists. 


N. 


S. 


E. 


VV. 


Deps. 


Sums. 


N. Areas. 


?. Areas. 


1 


N. 440 30' E. 


AB 
6-35 

HC 
4-03 

ID 
8-37 


A IV 
453 




AB" 
44() 




BB' 

4-40 


BB' 

446 


2 ABii' 
2d'2(W8 




o 


N. 740 30' E. 


B'C' 

1-08 




B"C" 

3-88 




CO' 

8-34 


BB'-fCC 

12-80 

OC'+DlV~ 

21-27 


a BbVO 

138240 




3 


S. 330 15' E. 




CD' 

7-00 


CD" 

4-50 




l»D' 
12-93 




2 CG'D'D 
148-8900 


4 


S. 5?o 45' VV. 


DF 
7-53 




D' ' 
4 02 




I)"F" 

0-37 


Fr' 
6-56 
GG' 

1-1-2 


DD'+KF' 
19-49 




2 DD'fr'F 
78-3498 


I 
5 


N. 650 W. 


EG 

600 


FG' 
•2-54 






F"G" 
544 


FF'+GG' 
7-68 


2 1 F'..'ii 
19 5072 




G 


N. 21Q-15' VV. 


(iA 
3-08 


G'A 

2-87 






G"A 
1*12 


000 


GG' 
1-12 


2 GG'A 
3-2144 










O'F' 
1J-02 


C'F' 
1J.02 


AD" 
12-93 


AD" 
1293 


33-41 


65-82 


2 AC'C S-f-2 A.L-VG 

53-7434 


2 0'ODFF' 
227-2393 



The eighth column gives the difference of departures of the 
several corners of the field, and the first corner or station A; 
that is, this column gives the perpendicular distances of the sev- 
eral corners of the field from the meridian passing through the 
first station of the field. This eighth column is calculated from 
the columns E. and W. as follows : take the departure of the first 
side for the first term of this column, which in the present case 
is an easterly departure. The departure of the second side, 
being easterly, is added to the former departure, thus giving 
the second term of this column. The third side also gives an 
easterly departure, which departure must be added, thus giving 
the third term of this column. The fourth side gives a westerly 
departure, which must therefore be subtracted, leaving for re- 
mainder the fourth term of this column. The departures of the 
fifth and sixth sides, being westerly, are to be subtracted in suc- 
cession. The last term of this column is obviously naught, since 
it is the perpendicular distance of the termination of the last 
side from the meridian passing through the first station ; but the 
termination of the last side is the same as the beginning of the 
first side, so that this distance vanishes. 

Had the first term of this column commenced with a westerly 



§ 75.] SURVEYING. Ill 

departure, then the westings would have been successively add- 
ed, and the eastings subtracted. 

The values of the ninth column are the sums of the values in 
the eighth column, and consequently represent the sum of the 
parallel sides of the trapezoids formed by perpendiculars drawn 
from the several corners of the field to the principal meridian. 
The first term being simply the perpendicular BB', since the 
perpendicular distance of the first corner from the meridian is 
naught, so also the last term is simply the perpendicular GG'. 
If, then, we regard the triangles ABB' and GG'A as trapezoids, 
having one of their parallel sides reduced to zero, we may then 
say that the perpendicular distances between the parallel sides 
of these several trapezoids will be the latitudes of the respective 
sides, as given in columns N. and S. 

If we multiply the values of this ninth column by the respec- 
tive latitudes, as given in columns ~N. and S., we shall obtain the 
double areas of these trapezoids, which double areas are given 
in the tenth and eleventh- columns. Those double areas obtain- 
ed by multiplying by a northing are placed in the column of 
N. Areas, and those found by multiplying by a southing are 
placed in the column of S. Areas. 

If we take the sum of the south areas, we shall obviously have 
double the area of C'CDFF', which, besides embracing the en- 
tire field, includes all that portion without lying between the 
sides of the field and the principal meridian. The sum of the 
north areas is the double of AC'CB + AF'FG, which is no por- 
tion of the field, but corresponds with that part of the sum of 
the south areas which has already been described as lying be- 
tween the sides of the field and the principal meridian. Hence, 
the difference between the sum of the north and south areas 
will be just double the area of the field, which, being divided by 
2, will give the area in square chains. 

We will now repeat the foregoing table, giving only the nu- 
merical values, as usually given by surveyors. 



112 



SURVEYING. 



[CHAP. IX. 



Nos. 


Bearings. 


Dists. 


N. 


S. 


E. 


W. 


Deps. 


Sums. 'N. Areas. 


S. Areas. 


1 

2 


N. 44° 30' E. 


6-35 


4-53 




4-46 




446 


4-46 


20-2038 




N. 74° 30' E. 


4-03 


1-08 




3-88 




8-34 


12-80 


13-8240 




3 


S. 33° 15' E. 


8-37 




7-00 


4-59 




12-93 


21-27 




148-8900 


4 
5 
6 


S. 57° 45' W 


7-53 




402 




6-37 


6-56 


19-49 




78-3498 


N. 56° 00' W. 


6-00 


2-54 






5-44 


112 


7-68 


19-50721 


N. 21° 15' W. 


3-08 


2-87 






1-12 


o-oo 


1-12 


3-2144 










1102 


11-02 


12-93 


12-93 


33-41 


66-8i! 


56-7494,227-2398 



227-2398 
56-7494 

2)170-4904 
Area = 85-2452 sg. chains. 

We will add the full work of a second example for the pupil 
to trace through, omitting the plot or diagram. 



Nos. 



Bearings. 



W. 40° E. 



S. 60° E. 



S. 25° E. 



Dists. 



10-00 



12-50 



8-10 



S. 57° W. 



11-80 



West. 



7-28 



N. 15|° W. 12-84 



N. 


S. 


E. 


w. 


Deps. 


Sums. 


N.Areas. 
49-2538 


S. Areas. 


7-66 




6-43 




6-43 


6-43 






6-25 


10-82 




17-25 


23-68 





148-0000 




7-34 


3-42 




20-67 


37-92 


278-3328 




6-43 




9-90 


10-77 


31-44 




202-1592 








7-28 


3-49 


14-26 






12-36 
20-02 






3-49 


o-oo 


3-49 


43-1364 




20-02 


20-67 


2067 


58-61 


117 22 


92-3902 


628-4920 



92-3902 

2)536-1018 

Ans. 268-0509 
sg. chains. 



§ 76. Since the 8th column, which gives the perpendicular 
distances of the several corners from the principal meridian, is 
formed by adding the eastings and subtracting the westings, or 
by adding the westings and subtracting the eastings, it is bet- 
ter always to commence this . addition at the most easterly or 
most westerly station of the field, otherwise we should have 
negative values in this column, which would lessen very much 



§76.] 



SURVEYING. 



113 



the simplicity of this method. A very little inspection of the 
columns E. and W. will indicate where to begin the additions. 

In the following example, we commenced forming the terms 
of the 8th column at the 6th station, which is the most easterly 
corner of the field, by adding the westings and subtracting the 
eastings. 



1 
Nos. 


Bearings. 


Dists. 


N. 


S. 


E. 


W. 


Deps. 


Suras. 


N. Areas. 


S. Areas. 


1 N.23°15'E. 


7-11 


6-53 




280 




14-00 


30-80 


201-1240 




2 S. 24°30'E. 


6-97 




6 34 


289 




11-11 


25-11 




159-1974 


3 N.40°45'E. 


728 


5-51 




4-75 




6-36 


17-47 


96-2597 




4 |S. 19° 15' W. 


1001 




945 




3-30 


9-66 


16-02 




151-3890 


5 


S. 60°30'E. 


11-10 




5-47 


9-66 




o-oo 


9 66 




52-8402 


6 


N.82°15'W. 


13-12 


1-77 






13-00 


13 00 


13-00 


23-0100 




7 S. 45°45'W. 


7*03 




4-90 




5 03 


18-03 


3103 




1520470 


8 |N. 10°15'E. 


8-99 


8-84 




1-60 




16-43 


34-46 


3046264 




9 IN. 6° 0' W. 


3-53 


3-51 






0-37 


16-80 


33-23 


116-6373 










26-16 


26-16 


21-70 


21-70 


10539 


210-78 


741-6574 
515-4736 


5154736 



2)2261838 



11-30919 Acres. 

It would have been equally well had we commenced at the 
8th or most westerly station, in which case we should add the 
eastings and subtract the westings. 

A principal meridian drawn through any other station, except 
the most easterly or most westerly, will evidently divide the 
field so that the perpendiculars from the corners upon this me- 
ridian will be part on the east and part on the west of this me- 
ridian, and consequently we should have negative values in our 
8th column, an inconvenience which we wish to avoid. Below 
we have repeated the computation of the last field, by com- 
mencing at the 8th station, and have added the eastings and 
subtracted the westings. The result is precisely the same as in 
the former case. 

8 



114 








SURVEYING. 






[CHAP. IX. 


Nos. 

1 


Bearings. 


Dists. 


N. 
6-53 


S. 


E. 


W. 


Heps. 


Sums. 


N. Areas 


I 
S. Areas. 


N. 23°15 r E. 


7-11 




2-80 




4-03 


526 


34-3478 




2 


N. 24°30'E. 


6-97 




634 


2-S9 




692 


10-95 




694230 


3 


N. 40° 45' E. 


7-28 


5 51 


4-75 




11-67 


18-59 


102-4809 




4 
5 
6 

7 
8 
9 


S. 19° 15' W. 


10-01 




945 




3-30 


837 


20-04 




189 3780 


S. 60° 30' E. 


11-10 




5-47 


9-66 




18-03 


2640 




144-4080 


N.82°16'.W. 


13-12 


1-77 


4-90 




1300 


5-03 


23 06 


40-8162 


S. 45° 45' W. 


7-03 






5-03 


000 
1-60 
1-23 


503 




24-6400 


N. 10°15'E. 


899 


8-84 


1-60 


1-60 


14-1440 




N. 6° O'W. 


3-53 


3-51 






037 


2-83 


99333 








26-16 


26-16 


21-70 


21-70 


56-88 


113-76 


2016722 


427-8560 
201-6722 








2 


)226-1838 




1180919 
sg. ch. 



§ 77. "When a survey has been accurately made, and all the 
latitudes and departures have been found without error, we 
must obviously have the following relations : 

First. The sum of the northings must equal the sura of the 
southings; and the sum of the eastings must equal the sum of 
the westings. 

Secondly. The sum of the departures as given in the 8th col- 
umn must be just one-half the footing of the sums, as given by 
the 9th column. 

In practice, we are, however, rarely able to work so close as 
to make the latitude and departure columns exactly balance. 
They may be made to balance by subtracting half their differ- 
ence from the greater values, and adding their half difference 
to the smaller values. As an example, take the following field : 



?•] 



SURVEYING. 



Nos. 
1 

o 


Bearings. 


Dists. 


N. 


s. 


E. 


W. 


Deps. 
7-29 


Sums. 


N. Areas. 


S. Areas. 


X46|° E. 


10-03 


6-87 
6-36 




7-30 
7-29 




7-29 


50-0094 




S. 79£° E. 


895 




1-63 


8-80 
8-79 




16-08 


2337 




380931 


3 

4 


N. P,7i° E. 


1048 


8-34 
8-32 




6-34 
6-38 




22 41 


3849 
51-60 


320-2368 




S. 20|° E. 


19-17 




17 93 

17-97 


6-79 
6 78 




29-19 




927-2520 


5 


S. 44|° W 


17-10 




12-14 
12-16 




1204 
12 06 


1713 


46-32 




563-2512 


6 

7 
8 

9 


West. 


3-49 








3-49 


13-64 


30-77 




■j 


North. 


5-80 


5-80 
5-79 








13-64 


27-28 


157-9512 


9 


N.75i° W. 8-87 


2-26 






858 
8-59 


5-05- 


18-69 


42-2394 




i\ T . 30i° W. 


993 


S 55 
8-53 






5-04 
5-05 


o-oo 


505 


43-0765 






31-82 
31-76 


31-70 
31-76 


29-23 ! 29 15 
291 9 |29'19 


124-43 


248-86 


613-5133 


1528-5963 
6135138 


.4m 


>)915 083O 
s 45*75415 



In this example, we see that the northings exceed the south- 
ings by 12 links. We have, therefore, subtracted 6 links from 
the northings, and added 6 links to the southings, observing to 
decrease and increase the latitudes in the ratio of their magni- 
tudes as near as can conveniently be done by inspection. In 
practice it will be found convenient to place the corrected values 
immediately under those thus corrected, as in the preceding 
table. 

In a similar manner we have balanced the eastings and west- 
ings by subtracting 4 links from the eastings and adding 4 links 
from the westings. 

Having balanced the latitudes and departures, we proceed 
with the rest of the work, as in the previous examples. 



116 



SURVEYING. 



[CHAP. IX. 



Rectangular Method of Plotting. 

§ 78. Having made known the rectangular method of com- 
puting areas of fields, we will now proceed to illustrate the rect- 
angular method of plotting. 

We will take the first field given, as an example : 

Draw upon the paper a rectangle or square, as NSLM, of suf- 
ficient size to embrace the plot. 

As the survey of this field was begun at its most westerly 
corner, we may assume NS as the principal meridian passing 
through the first corner of the field ; fixing upon the point A as 
the first corner of the field, and drawing WAE parallel toNM, 
it will represent the parallel of latitude from which the north- 
ings and southings are estimated. 




From the values given in the table, page 112, we find the lat- 
itudes and departures of the several corners as follows : 



§ 78.] SURVEYING. 117 



Latitudes. 




Departures. 




+ 4-53 . 


. (1) 


+ 4-46 . 


. (1) 


+ 1-08 




+ 3-88 




+ 5-61 * 


• (2) 


+ 8-34 . 


. (2) 


-7-00 




+ 4-59 




-1-39 . 


. (3) 


+ 12-93 . 


. (3) 


-4-02 




- 6-37 




-5-41 . 


- (±) 


+ 6-56 . 


• W 


+ 2-54 




- 5-44 




-2-87 . 


. (5) 


+ 1-12 . 


• (5) 


+ 2-87 




- 1-12 




o-oo . 


. (6) 


o-oo . 


. (6) 



The north latitudes we have considered as positive and the 
south latitudes as negative ; so also, we have considered the 
east departures as positive and the west departures as negative. 

By taking as above the algebraic sums of the latitudes and 
departures of the respective sides, we found the latitudes and 
departures of the respective corners of the field. The latitude 
as well as the departure of the 6th corner, which must of course 
coincide with the corner at which the survey was commenced, 
is nothing, since the principal meridian, as well as principal 
parallel of latitude, was assumed to pass through this corner. 

Take from a scale, with the compasses, the proper distance to 
represent the latitude, 4-4*53, of the extremity of the first side, 
and set it off towards the right, from !N". and S. respectively to 1 ; 
then draw a pencil line through 1 and 1, and it will represent 
the meridian passing through the extremity of the first side. In 
a similar manner set off 4-46, the departure of the extremity of 
the first side upward, from W. and E. respectively to 1 ; then 
drawing the horizontal line through 1 and 1, it will represent 
the parallel of latitude passing through the extremity of the first 
side. Hence B, the point of intersection of this meridian and 
parallel of latitude, is the extremity of the first side sought. 

In a similar manner we find C, the extremity of the second 
side of the field, by drawing the meridian 2, 2 at the distance 
+5*61 from NS, and the parallel of latitude 2, 2 at the distance 
of -r-8-34 above "WE. Continuing in this way, we are enabled 



118 SURVEYING. [CHAP. IX. 

to find all the corners of the field, observing to set off negative 
latitudes below WE, and negative departures, when any occur ? 
towards the left of NS. 

Having determined, in this way, upon a rough piece of paper, 
the respective corners of a field, we may lay it on a clean piece 
of paper, and by means of a sharp point, as of a pin, mark the 
corresponding corners on the new paper ; then joining these 
corners we shall have a correct representation of the field. 

§ 7 9 Examples in Rectangular Surveying. 
1. Required the area of a field bounded as follows : 



N. 


6°E 




5245 chains. 


West 




4-14 


cc 


S. 


/TlO 

• 4 


W. 


54-83 


cc 


K 


67-r 


E. 


6-00 


cc 



Ans. 25 T Vo acres. 



2. Required the area of a field bounded as follows : 
K 50i° E. 1*27 chains. 



S. 41° E. 1-04} " 

S. 7i°E. 0-60£ " 

S. 68i° W. 0-99 " 

K 41° W. 1-24| " 



Ans. 27 T 8 o 6 o rods. 



3. Find the area of the field having the following bound- 
aries : 

1ST. 511° E. 2-88 chains. 



S. 41° 


E. 


5-33 


S. 7J C 


E. 


6-29 


S. 68i° 


W. 


2-97 


K 41° 


W. 


3-74 


K 5C4- 


E. 


3-81 


K 41° 


W. 


4-00 


S. 49° 


W. 


0-27 


K41° 


W. 


2-00 



cc 
cc 
cc 
cc 
cc 
u 



Ans. 3 T 4 oV acres. 



§ TO.] 







SUEVEYING. 


1 


(4.) 


chains. 






(5.) 


chains. 


K 30|° E. 


5-17 






K 89f ° E. 


3-04 


K 73i° E. 


8-12 






K 9£°E. 


5-00 


S. 45° E. 


5*03 






S. 80J°E. 


0-42 


S. 20j°W. 


9-87 






K 9° E. 


21-50 


S. 55i°W. 


7-55 






• K 81° W. 


3-37 


N. 22f ° W. 


11-23 






S. 9i° .W. 


12-32 


Area 14 T 5 


qq seres. 




N. 87J° E. 


1-20 










S. 9i° W. 


7-38 


(6.) 


chains. 






N. 80^° W. 


113 


K 88i° W. 


1-25 






S. 9i° W. 


7-47 


K li° E. 


0-38 






Area SA 


. OR. 12P. 


N. 881° W. 


1-00 










K 8 D W. 


1-60 






(7.) 


chains. 


N. 80i° w. 


4-95 






K 30^° E. 


5-17 


K 4° E. 


2-41 






K 73i° E. 


8-12 


N. 89f° "W. 


0-81 






S. 45° E. 


5-03 


K 2|°E. 


6-00 






S. 20i° W. 


9-87 


S. 88° W. 


5-68 






S. 55i W. 


7-55 


S. 24° E. 


8-68 






K 32|° W. 


4-03 


1ST. 89i° E. 


2-01 






K. 17J° W. 


7-28 


S. H° E. 


1-30 






Area 14: A. 


SR. 31P. 


S. 84^°E. 


3-41 










S. 17i° E. 


1-44 






(8.) 


chains. 


S. 85J° E. 


0-38 






N. 40° E. 


10-00 


S. 4|° W. 


0-95 






S. 60° E. 


12-50 


S. 85i° E. 


3-66 






S. 25° E. 


8-10 


North 


1:10 






S. 57° W. 


11-80 


Area 4 


foo 3,cres. 




West 


7-30 










1ST. 15f° W. 


12-83 










Area 26A. SR. llf 






(9.) 




chains. 




t 


S. 


24i° 


E. 


6-97 






1ST. 


40f° 


E. 


7*28 






S. 


19i° 


W. 


10-01 






s. 


60i° 


E. 


11-10 






1ST. 


82i° 


W. 


11-65 






Br. 


9f° 


W. 


14-39 





119 



Area 5A. 2R. 25P. 



120 



SURVEYING. 



[CHAP. IX. 



§ 80. Suppose the bearing and length of one of the sides of 
a field not to be taken, on account of obstructions ; it is required 
to determine its bearing and length on the supposition that all 
the other sides have been accurately taken. 

As an example, suppose in a field of seven sides, as given be- 
low, we are required to supply the 5th side. 



1. N. 57° E. 

2. S. 74:° E. 

3. S. 20i° E. 

4. S. 24J° W 
5. 

6. S. 87° W. 3-56 

7. JST. 10J ° W. 11-12 



chains. 

4-04 

7-25 
3-87 
4-39 




Nos. 


Bearings. 


Dists. 


N. S. 


E. 


W. 


1 
2 

o 
o 


N. 57° E. 


4-04 


2-20 




3-38 




S. 74° E. 


7-25 




2-00 


6-97 




S. 20|° E. 


3-87 




363 


1-34 




4 


S. 24£° W. 


4-39 

(5-39) 




3-99 




1-82 


5 


(S. 52° W.) 




(3-32) 




(4-24) 


6 


S. 87° W. 


3-56 




0-19 




356 


7 


K 10|° W. 


11-12 


10-93 






2-07 



"We proceed to find the latitudes and departures of all the 
sides except the 5th, which values, when found, have been in- 
serted within parentheses. 

After adding the latitudes of all the sides except the 5th, we 



§ 80.] SURVEYING. 121 

find the northings to exceed the southings by 3*32, which is 
evidently the sonth latitude of the 5th side, since the sum of all 
the northings must equal the sum of all the southings of every 
field. In a similar manner, by adding the departures, we find 
the eastings to exceed the westings by 4*24, which is the west 
departure of the 5th side. 

Having found the latitude and departure of a line, we can 
find its bearing and length as follows : 



By § 41, we have 



-r, . Departure 

sin. .Bearing = — — ± • 

° Distance 



(!•) 



-r» . Latitude , n N 

cos. Bearing = (2.) 



Distance' 

Dividing (1) by (2), we have, [§ 8 (1), of equation B,] 

-T-, . Departure 

tans;. Bearing = T L . -^ — . 
& 5 Latitude 

Equation (1) immediately gives 

-r.. , Departure 

Distance = - — ^ : — . 

sin. Bearing 



(3.) 



(*•) 



If we use logarithms, equations (3) and (4) will give as fol- 
lows : 

From the logarithm of the departure increased by 10 subtract 
the logarithm of the latitude, and the result will be the logarithm 
of the tangent of the bearing, as given in Table II 

From the logarithm of the departure increased by 10 subtract 
the logarithmic sine of the bearing, and the result will be the 
logarithm of the distance. 

In the present example we have 

10 -flog. 4-24 = 10-627366 . . . 10*627366 
log. 3-32 = 0-521138 sin. 51° 56' = 9-896137 

log. tang. 51° 56' = 10-106228 log. 5*3855 = 0-731229 

Hence, the bearing taken to the nearest quarter of a degree, 
which is as close as can well be observed with the ordinary Sur- 
veyor's Compass, is S. 52° "W". The distance taken to the near- 
est link is 5*39 chains. 



122 



SURVEYING. 



[CHAP. IX. 



This same method will give the bearing and distance from 
any one corner of a field to any other corner. Using the fore- 
going held, for example, let it be required to find the line join- 
ing the 1st and 5th corners, that is, the line drawn from A to F. 



N<>3. 


Bearings. 


Dists. 


N. 


S. 


E. 


W. 


1 


N. 57° E. 


4-04 


1 2 20 




3-38 




o 


S. 74° E. 


7-25 




200 


6-97 




3 
4 
5 


S. *0i° E. 


3 87 


1 


3 63 


1-34 


I 


S. 2ii° W. 


439 


| 


3-99 




182 


(N. 53° W.) 


(12-35) 


(7-42) 






(9-87) 



10+ log. 9-87 = 10-994317 
log. 7-42 = 0-870404 



log. tang. 53° 4' = 10-123913 



. 10-994317 
log. sin. 53° 4' = 9*902729 



log. 12-348 = 1-091588 



§81. This same method will make known the distance of a 
line in a survey through a swamp, or across a body of water, or 
from one point to another, which is invisible by reason of some 
intervening obstruction. 

As an example, suppose in 
running the line AL, S. 37° 
E., we come to the edge of a 
swamp at B. We make our 
way around the swamp by 
the most easy route, noting 
the bearing and distance at 
each change of direction, un- 
til we reach a point H, which 
we judge to be nearly on the 
line AL. Then taking the 
latitudes and departures of 
BC, CD, DF, FG, and GH, 
we are enabled to find the 
line BH, as in preceding ex- 
amples. 

Suppose the bearings and distances of these lines to be as 
follows : 




82.] 



SURVEYING. 



123 



Nos. Bearings. 


1 
Dists. | 


N„ 


s. 


E. 


W. 


1 BC. N. 75^° E. 


10-33 : 


2-63 




999 


2 CD, S. 40±° E. 


6-40 




4-86 


4-16 


1 3 I DF, S. 72i° E. 


483 1 


j T47 


4-60 


4 | FG, S. 15|° W. 


11-26 




1084 




306 


5 j GH,S. 8o£° W. 


2'4fi 


0-41 




2'42 


6 ! HB, (N. 41|° W.) 

i 


(19-99) 

1 


(,14-95) i 
1 




(13-27) 



10+ log. 13-27 = 11-122871 
log. 14-95 = 1-171641 



11-122871 
sin. 41° 35' 35" = 9*822060 



tang. 41° 35' 35" = 9-948230 



log. 19-9899 



1-300811 



Since the reversed bearing of HB, which is the bearing of 
BH, is greater than the bearing of AL, it follows that we have 
not yet, at IT, reached the line AL. Had the bearing of BH 
been less than that of AL, it would have made known that the 
part H was on the opposite side of the line AL. If we suppose 
HK to be drawn perpendicular to AL, we shall have [Chap. III., 
Case L, eq. (1)] 

HK = BH x sin. HBK ; BK = BH x cos. HBK. 

The angle HBK = 41° 35' 35"- 37° = 4° 35' 35". 



log. BH = 1-300811 
sin. 4° 35' 35" = 8-903514 



1-300811 
cos. 4° 35' 35" =9-998615 



log. HK= 0-204325 
HK = 1-61, nearly. 



log. BK = 1-299426 
BK = 19-93, nearly. 



Since HK is perpendicular to AL, whose bearing is known, 
we readily find (§ 69) the bearing of HK to be S. 53° W. 

If, then, from the point H, in the direction of S. 53° "W"., we 
measure a distance of 1*61 chains, we shall reach the line AL at 
K, whose distance from B has already been found. 



§ 82. To survey a field bounded by irregular lines, by means 
of offsets. 

In the adjacent field suppose the west side from H to A to be 
bounded by an irregular line, as, for instance, a stream of wa- 
ter. Run a straight line from H to A ; then, by the method 



124 



SURVEYING. 



[CHAP. IX. 



already explained, compute the area included within the straight 
lines. 

Now, to obtain the area included between the straight dotted 
line HA and the irregular boundary, we measure offsets at right 




angles to HA at certain points, as at 1, 2, 3, 4, 5, &c, and then 
compute this area by the Scholium under Prob. IV., Chap. V. 
As an example, suppose we have given as follows : 









chains. 


AB, 


K57° 


E. 


4-04 


BC, 


S. 74° 


E. 


7-25 


CD, 


S. 20J C 


E. 


3-87 


DF, 


S. 24i c 


W. 


4-39 


FG, 


S. 52° 


W. 


5-39 


GH, 


S. 87° 


W. 


3-56 



HA, K 10}° W. 11-12 



OFFSETS. 






links 


At 


1, 


53 


a 


2, 


97 


« 


3, 


91 


a 


4, 


103 


a 


5, 


114 


u 


6, 


98 


a 


7, 


57 


a 


8, 


92 


u 


9 5 


77 


a 


10, 


48 



The offsets are all made at equal intervals along the line HA, 
each distance being 100 links, except the last from 10 to A 5 
which is 112 links. 



§S2.] 



SURVEYING. 



125 



The area within the straight lines is found as follows : 



Nos.j Bearings. 


Dists. 


N. 


S. 


E. 


W. 


Deps. 


Sums. N. Areas. 


S. Areas. 


1 | N. 57° E. 


4-04 


2-20 | 


3-38 




3-38 


3-38 7-4360 




2 | S. 74° E. 


7-25 


2-00 


6-97 




1035 


1373 


27-4600 


3 I S. 2(H° E. 


3-87 


| 3-63 


1-34 




11-69 


22-04 ! 


80-0052 

i 


4 


S. 24 i° W. 


4-39 




3-99 




1-82 


9-87 


21-56) 


86-0244 1 

i 


5 j S. 52° W. 


5-39 




3-32 




4-24 


5-63 


15-50 j 


51-4600 


6 

7 


8. 87° W. 


3-56 


| 0-19 




3-56 


2-07 


7-70 j 


1-4630 : 


N. 10|° W. 


11-12 


10-93 




2-07 


0-00 | 2-07 22-6251 










13-13 


13-13 


11-69 


11-69 


42-99 


85-98.30-0611 


246-4126 i 
30-0611 



2)216-3515 
108-17575 

The area of ten of the trapezoidal spaces, funned by the offsets, 
are readily found by the Scholium already referred to, observing 
to consider the offset at H as zero. Thus, 

53+97+91+103+114+98+57+92+77+1 of 48=806 links. 
And 8-06 x l'OO = 8'06 sq. chains. 

The last space, having 1*12 chains for its breadth, may be re- 
garded as a right triangle, the sides being 48 links and 112 links ; 
hence its area will be 1*12 X 0*24 = 0*2688 sq. chains, which 
added to 8*06 gives 8*3288 sq. chains for the entire area be- 
tween the dotted line and irregular boundary. This must be 
added to the portion included within the field as above com- 
puted. So that 108*17575 + 8*3288 = 116*50455, is the whole 
number of sq. chains sought, which gives ll^L 2i?. 24P. for the 
area of the whole field. 

When the straight line, which is run near the irregular side 
of a field, lies wholly without the field, then the offset areas 
must be subtracted from the area lying within the straight lines. 
It will frequently be found convenient to run the straight line 
so that it will cross the irregular boundary in one or more 
points ; in such cases some of the offset areas must be added 
and others subtracted. 



126 



SURVEYING. 



[CHAP. X. 



CHAPTER X. 

§83. Problems on the Division of Land. 



PROBLEM I. 

From a given point in tlie perimeter of a field, to draw a line 
so as to cut off a given area. 

Suppose the survey of the given 
field to be as follows : 

chains. 

1. 1ST. 30}° E., 5-17 

2. K 73J° E., 8-12 

3. S. 45° E., 5-03 

4. S. 20^° W., 9-S7 

5. S. 551° W., 7-55 

6. N. 32f° W., 4-03 

7. N. 17i° W., 7-23 

First. Compute the entire area of the field as below : 




Nov Bearings. 

1 ;N.30i°E. 

' 

2 ;N.73|°E. 

3 S. 45° E. 

4 S. 20 i° W. 

5 jS. 55i° VV. 

6 N.32f°W. 

: 

7 N. I7i° VV. 


Dists. 
517 



8 12 


N. 

! 


p. 


E. 


W. 


Hops. 


Sums. 


N. Areas. ' S Areas. 


4-47; 


2-61 




2-61 
1040 


| 2-61 

1301 


11-6667 | 


j 2-30, 


7 79 




29-9230 


5 03 


| 3 56 


3-56 




13 96 
10-54 


24 36 
2450 
14-88 


| 86-7216 


987 
7'55 
4-03 


| 9 26 




3 42 


,2-26-8700 


| 4 30 




6-20 


4-34 
216 

o-oo 

44 01 


| 63 9840 


3-39 i 




218 


6-50 

2 16 

88-02 | 


22-0350 


7 -AS | 


6 96 i 


2-:6 


15 0336 




1 


17-12 


17-12, 


1396, 


13 90 j 


7865S3 3775756 
j 78 6583 



2)2989173 
Area, sq cliuius 14945S65 

Half the field, or the area ABCDX= 74-729325. \ 

As a particular case, let it be required to draw from the first 
corner of the field the line AX so as to divide the field into two 
equal parts. 



§83.] 



SURVEYING. 



127 



By inspecting the plot of the field, we judge the point X to 
be somewhere in the 4th side, DF. We then suppose the 1st 
and 4th corners to be joined, and proceed as below to calculate 
the area ABCD (Chap. XL, § 8)). 



Nos. 


Bearings. 


Dists. 


N. 

t47 

2-30 

077 


S. 


E. 


W. 


D«ps. 


Sums. 


ST. Area?. S. Areas, j 


1 


N 30i° E. 


5-17 




261 




2-61' 


261 
13-01 


11-0667 


o 


N. 73£°E, 


8 12 




7-79 




1 U-4U 


29-9230 


3 
4 


S. 4 5° E. 


5-03 


3 56 


3-56 




13-96 


2436 


80-7216 


[S.77°3' W.] 


[14-32 j 


[321] 




[13-96] 


o-uu 

26 97 


13-96 


j 44-8116 








6-77 


1396 


1396 


53 94 


41-5897 131-5332 | 
41-5897 1 



2) 9 94::5 
Area, sq. ch. 4497 175 



Area ABCDX = 74-729325 
" ABCD =44-97175 



" ADX = 29-757575 = area of triangle ADX, 
which requires to be added to the portion ABCD already cut off. 

In this triangle we have the area A. the side AD = s = 14-32 
chains, and the angle ADX = a = 56° 48', § 69, to find the side 
DX=^. 

By Prob. III. of Chap. Y., we have 

log. A = log. x + log. s + log. sin. a- 10-301030. 

Hence by transposition, and using arithmetical complements, 
we have 

log. x = 10*301030 + log. A +ar. co. log. s-f-ar. co. log. sin. a. 

Hence, when we have given the area of a triangle, one of the 
angles, and one of the adjacent sides, we may find the other 
adjacent side by this 

RULE. 

To the constant 10-301030, add the logarithm of the area, the 
ar. co. logarithm of the given side and the ar. co. logarithm of 
the sine of the angle, the sum will be the logarithm of the side 
sought. 



128 



SURVEYING. 



[chap. X. 



Applying the above rule, we have 

constant = 10-301030 

log. 29-757575 - 1-173596 

ar. co. log. sin. 56° 48' = 0-077397 

ar. co. log. 11-32 = 8-814057 



log. x = 0-696080 
x = 4*967 ; that is, the distance DX = 4'97 chains nearly. 

To prove that the portion ABCDX contains one-half the en- 
tire field, we will calculate its area by the rectangular method, 
as follows : 



N09. 


Bearings. 


Dists. 


N. 


S. 


E. 


W. 


Deps. 


Sums. !N. Areas. 


S. Areas. 


1 


N. 30i° E. 


5-17 


4-47 




2-61 




2-61 


2-61:11-6667 




2 


N. 73|° E. 


8-12 


2-30 




7-79 




] 0*40 


13-01 29-9230 

I 


3 


S. 45° E. 


5-03 




3'56 


3*56 




13-96 


24-36 


86-7216 


4 
5 


S. 2(H° W. 


4-97 




4-66 




1-72 


12-24 


26-20 




122-0920 






(1-45) 






(12 24) 


o-oo 


12-24 17-7480 








i 

1 


8-22 


8-22 


13-96 


13-96 


39-21 


78-42 


59-3377 


208-8136 
59-3377 



This area is merely a trifle too large. 



2)149-4759 
Area, sq. chains 7473795 



PROBLEM II. 

The direction of a line being giv- 
en, to find its position so that it 
may cut off a given area from a 
given field. 

Suppose the field to be the same 
as in last problem. Required to 
draw a line YX from the side BC 
to the side DF in the direction of 
S. 51J° E. so that the portion 
YCDX may be 2 acres. 

Draw DL parallel to XY, also 
produce BC and FD until they 
meet in K. 




§ 83.] SURVEYING. 129 

From the bearings of the lines we deduce (§ 69) the following 
angles : 

KCD = 61° 30' LCD = 118° 30' 

KDC = 65° 15' LDC = 6° 30' 



CKD = 53° 15' CLD = 55° 



180° 180° 

Triangle KCD gives 

sin. 53° 15' : sin. 61° 30' : : 5*03 : KD == 5-5169, 
sin. 53° 15' : sin. 65° 15' : : 5*03 : KC = 5*701. 

ar. co. sin. 53° 15' = 0-096230 . . . 0-096230 
sin. 6° 30' = 9-943899 sin. 65° 15'= 9-958154 

log. 5-03 =0-701568"] . . . 0-701568 

log. KD = 0-741697 \ log. KC = 0-755952 

sin. 65° 15' = 9-958154 j 

log. of double area = 1-401419 
log. 2 ,= 0-301030 

log. of area KCD = 0-100389, and area KCD = 12-60. 

Triangle LCD gives 

sin. 55° : sin. 118° 30' : : 5-03 : LD. 

ar. co. sin. 55° = 0*086635 
sin. 118° 30' = 9-943899 
log. 5-03 = 0-701568^1 



X 

sin. 6° 30' =9-053859 J 



log. LD = 0-732102 



0-487529 
0-301030 



log. of area LCD = 0-186499, and LCD = 1-5363. 

Area KCD + area LCD = 12-60 + 1-5363=14-1363 = area KLD. 
Area KCD + 2 acres = 12-60 + 20 = 32-60 = area KXY. 

14-1363 : 32-60 : : KD 2 : KX 2 , 
14-1363 : 32-60 : : LD 2 : XY 2 . 

9 



130 



SURVEYING. 



[chap. X. 



ar. co. log. 14-1363 = 8*849663 

log. 32-60 =1-513218 

twice log. KD = 1-483394 

2)1-846275 

log. KX = 0-923137 

KX = 8-3779 
KD = 5-5169 

DX = 2-861 



8-849663 

1-513218 

2 log. LD = 1-464204 



2 ) 1-827085 



log. XY = 0-913542 
XY = 8-1948 



That the position of this line XY is correctly found, may be, 
proved by computing the area of the triangle KXY. 

By the bearings of the lines we find (§ 69) the angle KXY = 
71° 45' ; hence, the area of the triangle KXY may be computed 
by Second Eule of Problem III., Chap. Y., as follows : 

log. KX = 0-923137 

log. XY = 0-913542 

log. sin. 71° 30' = 9-977586 

1-814265 
0-301030 



log. area KXY = 1-513235, which agrees nearly 
with 1-513218, which is the log. of 32-60, the exact area. 



LEMMA. 

Tlirough a given point P, to draw a straight line ED to cut 
two straight lines AB, A O, 
given in position, but not 
parallel, so that the triangle 
ADJE, thus formed, may 
be of a given area. 

Through P draw FPI par- 
allel to AB, intersecting 
AC at F; and upon AF 
construct the parallelogram 
AFHI, equal in area to the 
given area of the triangle. 
Draw IK perpendicular to 
AI, and equal to FP ; and, 
from the point K to AB, ap- 




/ 


/ 




/ 


/ 




/ • 




/ s 




/ / 




/ / 








'// 





§83.] 



SURVEYING, 



131 




K u 



ply KD=PH ; then through D and P draw DE, and the problem 
will be solved. 

For, supposing Fi s- 2 - 

M to be the inter- 
section of DE and 
IH, it is evident, 
because of the 
parallel lines, that 
the three triangles 
PHM, PFE, and 
MDI are equian- 
gular. Therefore, 

the area of all equiangular triangles being in the ratio of the 
squares of their homologous sides (B. IV., Prop. XYL), and 
the sum of the squares of FP or IK and DI being equal to the 
square of PH or KE> by construction (B. II., Prop. VIII.), it is 
evident that the sum of the triangles PFE and DMI is equal to 
the triangle PHM (this is obvious also from B. IV., Prop. XX., 
Cor.) ; to which equal quantities in fig. 1, add AFPMI, and we 
shall have ADE equal to AFHI. But in fig. 2, let PFE be 
taken from PHM, and there will remain EFHM = DMI ; to 
each of which, adding AIME, we have AFHI = ADE as before. 

In fig. 1, if the point D is taken on the left of I as at D', the 
line D'E' drawn through P will also satisfy the conditions of the 
problem. For, the sum of the triangles PFE' and D'M'I is 
equal to the triangle PHM'. [Now let D'M'I be taken from 
PHM', and there will remain PHID' = PFE' ; to each of which, 
adding AD'PF, we shall have AFHI = AD'E', as already 
given. 

Cor. From this we see that when the point P is within the 
angle BAC, as in fig. 1, there will in general be two solutions. 
If, however, the point P is at the middle of FH, then the line 
KD will equal KI, and the two points D and D' will unite with 
the point I, in which case there will be but one solution. If 
PH is less than PF, KD will not reach the line AB, and the 
problem will be impossible. 

In fig. 2 there will always be one solution, and only one. For 
KD, or its equal PH, is equal to the sum of PF and FH ; that 
is, equal to the sum of KI and IA, and therefore KD cannot 
meet the line AB on the left of I between I and A, for if it did 



132 



SURVEYING. 



[chap. X, 




we should have the hypotenuse of a right-angled triangle greater 
than the sum of the two sides, which is impossible. 

Scholium. The solution of the following problem may be ob- 
tained as follows : Fig. a 

Through a given point P 
to draw a straight line EI 
to cut two straight lines AB, 
AC, given in position, so 
that the area of the triangle 
AEImay he the least pos- 
sible. 

Through P draw FH par- 
allel to AB, make PH equal 
to FP, and draw HI paral- 
lel to AC ; through I and P draw IE, and the triangle will be 
the least that can be formed by a line passing through P. 

We are now prepared for the solution of our 

PROBLEM III. 

Through a given point either within or without the perimeter 
of afield, to draw a line so as to cut off a given area. 

CASE I. 

When the point is within the field, as at P. 

Let ABCDFGH be the 
same field as in the pre- 
ceding problems. 

Produce the sides BC 
and FD until they meet at 
K Through P draw MPN 
parallel to BK, and make 
the parallelogram MKRK" 
equal to the area of the 
triangle DCK added to 
the area to be cut off. 
Through B draw PT per- 
pendicular to BK, and 
equal to PM ; draw TX 
equal to PN, and through 
X and P draw XPY, and 




§ 83.] SURVEYING. 133 

it will be the line required : all of which is obvious from the 
preceding Lemma. 

CALCULATION. 

As an example, suppose the bearing of CP to be S. 2° W., 
and equal to 3*75 chains, and that the area to be cut off is 2 acres. 

Triangle CPD gives 

CD = 5-03 ; CP = 3*75 ; and the contained angle DCP = 47°. 
5-03+3-75=8-78 ; 5-03-3-75=l-28 ; } (180° -47°) = 66° 30'. 

8-78 : 1-28 : : tang. 66° 30' : tang. 18° 32' nearly. 

ar. co. log. 8-78 = 9*056505 66° 30' 

log. 1-28 = 0-107210 18 32 

tang. 66° 30' = 10*361698 g5 o 2 / = CPD 

tang. 18° 32' 8" = 9-525413 47 58 = CDP. 

sin. 47° 58' : sin. 47° : : 3'75 : PD = 3-692. 

ar. co. sin. 47° 58' = 0-129154 
sin. 47° = 9-864127 
log. 3-75 = 0-574031 

log. PD = 0-567312 

From the bearings of PC and of PM, which is parallel to BC, 
we find 73° 30'— 2° =71° 30', for the angle CPM ; hence, 
85° 2' - 71° 30' = 13° 32' = angle MPD. The angle PMD is 
equal to the angle at K == 53° 15'; consequently, the remaining 
angle PDM of the triangle PDM is = 113° 13'. 

sin. 53° 15' : sin. 13° 32' : : PD : DM = 1-078, 
sin. 53° 15' : sin. 113° 13' : : PD : PM =4-235. 

ar. co. sin. 53° 15' = 0-096230 . . . 0-096230 
sin. 13° 32' = 9*369236 sin. 113° 13' = 9-963325 
log. PD =0-567312 . . . 0-567312 



log. DM = 0-032778 log. PM = 0-626867 

DK-DM=5-517-l-078=4-439=MK, one side of parallelogram. 
Area KCD + 2 acres=12-60+20=32-60=area of parallelogram. 

If we denote the area of this parallelogram by A, the angle 



134 SURVEYING. [CHAP. X. 

at Kby a, and the side KM by s, and the other adjacent side 
KR by x, we shall have, by Prob. II. of Chap. Y., 

log. A = log. a? + log. s + log. sin. a— 10, 

which, by transposition, gives 

log. x = 10 + log. A + ar. co. log. s + ar. co. log. sin. a. 

Hence, when we have given the area of a parallelogram, one 
of the angles, and one of the adjacent sides, we may find the 
other adjacent side by this 

RULE. 

To the constant 10, add the logarithm of the area, the ar. co. 
logarithm of the given side, and the ar. co. logarithm of the sine 
of the angle, the sum will he the logarithm of the side sought. 

Applying the above rule, we have 

constant — 10* 
log. 32-60 = 1-513218 
ar. co. log. 4-439 = 9-352715 
ar. co. sin. 53° 15' = 0*096230 



log. KR = 0-962163, and KR= 9-166= side of parallel- 

PM=4-235=TR [ogram. 

P]sr=4-931=TX=TX' 
TX 2 -TR 2 = (TX + TR) x (TX-TR) = RX 2 . 

TX + TR = 9-166, log. = 0-962163 
TX - TR = 0-696, log. = 1-842609 

2) 0-804772 = log. RX 2 

log. RX = 0-402386, and RX = 2-526 

KX = KR - RX = 9-166-2-526 = 6-64. 

OX = KX - KC = 6-64 - 5*701 = 0-939, or about 94 links. 

CX' = CX + 2 RX = 0-939 + 5-052 = 5-991. 

Having found the points X and X', we may readily run the 
line from these points through the given point P, provided there 
is nothing to prevent our seeing P from the points X and X ; . 

When desired, the bearings and lengths of these lines may be 
found as follows : 



§ 83.] SURVEYING. 1.35 

In the triangle CPX we have CP = 3*75 ; CX = 0*939 ; and 
the included angle PCX = CPM = 71° 30'. 

Hence, 3«75 +0*939 = 4*689 ; 3*75-0*939=2-811 ; J (180°- 
71° 30') = 54 15'. 

4-689 : 2-811 : : tang. 51° 15'. 

ar. co. log. 4-689 = 9-328920 54° 15' 0" 

log. 2-811 = 0-448861 39° 47' 8" 

tang. 54° 15' = 10142730 mm = fiTyf, = ^ cxp 

tang. 39° 47' 8" = 9-920511 

The bearing of XC is K 73° 30' E. ; hence 180° -(73° 30' + 
94° 2' 8") = 12° 27' 52", so that XT is S. 12° 28' E. nearly. 

In the triangle CPX', we have CP = 3-75 ; CX' = 5-991 ; and 
the included angle PCX'=71° 30'. Hence 5-991 + 3-75=9-741 ; 
5-991-3-75 =2-241 ; \ (180°-71° 30') = 54° 15'. 

9-741 : 2-241 : : tang. 54° 15'. 

ar. co. log. 9-741 = 9-011396 

log. 2-241 = 0-350442 54° 15' 0" 

tang. 54° 15' = 10-142730 17° 43' 21" 

tang. 17° 43' 21"= 9-504568 diff.=36° 31' 39"=angle CX'P. 

180° -(73° 30' + 36° 32') = 69° 2' ; hence, X'Y' is S. 69° 2' E. 

The triangles KXY and KX'Y' give 

sin. 32° 42' 52" : sin. 53° 15' : : 6'64 : XY. 
sin. 90° 13' 21" : sin. 53° 15' : : 11-692 : X'Y'. 



ar. co. sin. 32° 42' 52"=0*267216 ar.co.sin.90° 13' 21"=0'000003 
sin. 53° 15' =9-903770 .... 9-903770 
log. 6-64 =0-822168 j log. 11-692=1-067889 

log. XY=0-993154 \ log. X'Y'=0'971662 

sin. 94° 2' 8" = 9*998832 ' sin. 36° 31' 39" = 9*774669 



1*814154 1*814220 

0*301030 0*301030 



log. area KXY=1-513124 log. area KXY'=1*513190 

XY=9*8436. X'Y'=9-3683. 

Each of the above logarithms agrees nearly with 1*513218, the 
log. of 32*60. Hence the position of the lines XY and X'Y' have 
been correctly determined. 



136 



SURVEYING. 



[CHAP. X. 



CASE II. 



When the point is without the field, as at P. 

Let ABCDFGH be the same 
field as in Case I. 

Produce the sides BC and FD 
until they meet at K. 

Through P draw PME" par- 
allel to FK, and make the par- 
allelogram MNRK equal to the 
area of the triangle DCK added 
to the area to be cut off. Through 
E draw ET perpendicular to FK 
and equal to PM ; draw TX 
equal to PN, and through X 
and P draw XYP, and it will be the line required ; as is evi- 
dent from the preceding Lemma. 




CALCULATION. 

As an example, suppose the bearing of BP to be !N". 55° 30' 
E., and equal to 5*35 chains, and that the area to be cut off is 
2 acres. 

Triangle BPC gives 

BC = 8-12 ; BP = 5-35 ; and the contained angle 18°. 
8-12 + 5-35 = 1347; 8-12-5-35 - 2*77 ; J (180°-18°) - 81°. 
13-47 : 2-77 : : tang. 81° : tang. Jdiff. 



ar. co. log. 13-47 = 8-870632 



log. 2-77 
tang. 81° 



0-442480 
10-800287 



tang. 52° 23' 48" = 10-113399 

sin. 28° 36' 12" : sin. 18 c 



81° 

52° 23' 48" 

133° 23' 48" = angle BPC. 
28° 36' 12" = " BCP. 

: 5-35 : PC = 34533. 



ar. co. sin. 28° 36' 12" - 0-319898 

sin. 18° = 9-489982 

log. 5-35 = 0-728354 

log. PC = 0-538234 

From the bearings of PB and of P2ST, which is parallel to DF, 
we find 55° 30' -20° 15' = 35° 15', for the angle BPM ; hence, 



§ 83.] SURVEYING. 137 

133° 23' 48"-35° 15' = 98° 8' 48" = angle MPC. The angle 
PMC is equal to the angle at K = 53° 15' ; consequently, the 
remaining angle PCM of the triangle PCM is 28° 36' 12", same 
as BCP. 

sin. 53° 15' : sin. 98° 8' 48" : : PC : CM = 4-2664, 
sin. 53° 15' : sin. 28° 36' 12" : : PC : PM = 2-0633. 

ar. co. sin. 53° 15' = 0-096230 . . . 0*096230 

sin. 98° 8' 48" = 9-995595 sin. 28° 36' 12" = 9-680102 

log. PC = 0-538234 . . . 0-538234 

log. CM = 0-630059 log. PM = 0-314566 

GK+OM=5-701-H:-266=9-96T=MK=one side of parallelogram. 
Area KCD+2 acres=12-60+20=32-60=area of parallelogram. 

Proceeding to find the other side of the parallelogram, as in 
Case I., we have 

constant = 10* 
log. 32-60 = 1-513218 
ar. co. log. 9-967 =■ 9-001436 KE = 4-0821 
ar. co. sin. 53° 15' = 0-096230 PM = 2-0633 = TE. 



log. KE = 0-610884 PN = 6*1454 = TX. 

TX 2 -TE 2 = (TX + TR) x (TX -TR) = EX 2 . 

TX + TR = 8-2087, log. = 0-914274 
TX - TR = 4-0821, log. = 0-610884 

2) 1-525158= log. EX 2 , 

log. EX = 0-762579, and. EX = 5-7887. 
KX = KE + EX = 4-0821 + 5-7887 = 9-8708. 
DX = KX - KD = 9-8708 - 5-5169 = 4-3539. 

Having found the point X, we proceed to find the bearing 
and length of XY as follows : 

In the triangle CDX we have DC = 5*03 ; DX =4-3539; 
angle CDX = 114° 45' ; hence (Theorem II., Chap. IV.), 
9-3839 : 0-6761 : : tang. 32° 37' 30" : tang. 2° 38' 26". 
ar. co. log. 9-3839 = 9-027617 32° 37' 30" 

log. 0-6761 = 1-830011 2° 38' 26" 

tang. 32° 37' 30" = 9-806276 35 o 15 , 56 „ = J)XC 

tang. 2° 38' 26" = 8-663904 29° 59' 4" =DCX. 



138 SURVEYING. [CHAP. X. 

sin. 35° 15' 56" : sin. 114° 45" : : 5-03 : OX = 1-9117. 

ar. co. sin. 35° 15' 56" = 0*238548 

sin. 114° 45' = 9-958154 

log. 5-03 = 0-701568 



log. CX = 0-898270 

In triangle PCX we have CX = 7-9117 ; CP = 3*4533 ; angle 
PCX - BCD + BCP-DCX = 118° 30' + 28° 36' 12"-29° 59' 
4" = 117° 7' 8" ; hence (Theorem II., Chap. IV.), 

11-365 : 4-4584 : : tang. 31° 26' 26" : tang. Jdiff. 

ar. co. log. 11-365 = 8-944430 31° 26' 26" 

log. 4-4584 = 0-649179 13° 29' 13" 

tang. 31° 26' 26" = 9*786307 17° 57' 13" = CXP 
tang. 13° 29' 13" = 9-379916 

Angle DXP = DXC + CXP = 35° 15' 56" + 17° 57' 13" == 
53° 13' 9" ; hence 53° 13' 9" -20° 15' = 32° 58' 9" ; that is, the 
line XY bears K 32° 58' 9" W. 

Triangle KXY gives angle KYX = 73° 31' 51" ; and we have 

sin. 73° 31' 51" : sin. 53° 15' : : 9-8708 : XY = 8-2474. 

ar. co. sin. 73° 31' 51" = 0-018194 

sin. 53° 15' = 9*903770 

log. 9-8708 = 0-994352 



log. XY - 0-916316 t 
sin. 53° 13' 9" =9-903596 



1-814264 
0-301030 



log. area KXY = 1-513234 

This logarithm, by agreeing so closely with 1-513218, the log. 
of 32*60, proves the foregoing work to be correct. 

In the foregoing problems the work has been carried to a 
greater degree of accuracy than necessary. For ordinary pur- 
poses angles smaller than minutes of a degree may be neglected, 
so also may distances which do not exceed one-tenth of a link. 



84.] SURVEYING. * 139 



§ 8 4. Examples of the Division of Land. 

1. Given the boundaries of a field as follows : 1. E". 30|° E. 
5-17 chains ; 2. K 73±° E. 8*12 chains ; 3. S. 45° E. 5-03 chains ; 

4. S. 20i° W. 9-87 chains ; 5. S. 55-}° W. 7"55 chains ; 6. K 22f ° 
W. 11*23 chains. It is required to draw a line from the first 
corner to meet the fourth side so as to divide the field into two 
equal parts. At what distance, measured from the fourth cor- 
ner, will this line intersect the fourth side \ 

Ans. 4*64 chains. 

2. In the same field as above, it is required to draw a line 
1ST. 80° E., intersecting the 4th and 6th sides so as to divide the 
field into two equal parts. At what distance from the 4th cor- 
ner will this line intersect the 4th side? Ans. 2*85 chains. 

3. A field is bounded as follows : K 46i° E., 10-03 eh. ; S. 
79i° E., 8-95 ch. ; K 37° E., 1048 ch. ; S. 20J° E., 19-17 ch. ; 

5. 44i° W., 17-10 ch. ; West, 3-52 ch. ; North, 5-69 eh. ; K 75° 
W., 8-87 eh. ; IN". 30J° W., 9-93 ch. Eequired to divide this 
field into two equal parts by a line drawn from the third corner 
to the sixth side. At what distance from the sixth corner will 
it intersect the sixth side % Ans. 64 links. 

4. What will be the bearing and length of the dividing line 
as found in the last example ? Ans. S. 1° E., 21*80 ch. 

5. The three consecutive sides of a field are as follows : AB, 
K 47° E. ; BC, S. 57° E., 21-10 ch. ; CD, S. 28f ° W. A line 
is to be drawn from the first side to the third side in the direc- 
tion of S. 45° E., so as to cut off 20 acres. From what point in 
the first side must this line be drawn ? 

Ans. At the distance of 6*61 eh. from the corner at B. 

6. The three consecutive sides of a field are as follows : AB, 
S. 791° E. ; BC, S. 30{° W., 10-14 ch. ; CD, S. 80i° W. It is 
required to draw a line S. 10|° E., intersecting AB and CD re- 
spectively in the points M and !N", so that the area MBCN may 
be just 5 acres. Required the distance BM. 

Ans. BM = 8-74 ch. 

7. In the same field as in last example, through a point P, 
which bears from B, S. 75 10 W., at a distance of 8*81 chains, it 
is required to draw a line so as to cut off 8 acres. Where will 
this line meet CD ? Ans. At 10*61 ch. from C. 



140 SURVEYING. [CHAP. XI. 

8. The boundaries of a field are as follows : K 20^° E., 10-13 
ch. ; S. 75i° E., 14-11 ah. ; S. 19J° W., 8-75 ch. ; S. 75^° W., 9-89 
ch. ; N. 441° W., 6*76 ch. Required to draw a line from the 
second side to the fourth side in the direction of S. 15° 13' W., 
so as to cut off from the eastern side of the field 5 acres. From 
what point in the second side must this line be drawn ? 

Ans. At the distance of 5*35 ch. from the 3d corner. 

9. In the same field, as given in the last example, there is a 
spring of water in the direction of S. 72J° "W". from the third 
corner, at a distance of 6*30 chains. It is required to draw a 
line through this spring intersecting the second and fourth sides, 
so as to cut off from the eastern side of the field 5 acres. At 
what distance from the fourth corner will this line meet the 
fourth side ? Ans. 5*56 ch. 



CHAPTER XI. 

§ 85. Miscellaneous Problems, useful to the Surveyor. 

PROBLEM I 

Let ABCbe a triangular field, and c 

8 a well within it ; it is required to ^& 



divide the field into two parts by a A ^^^K h 
line passing through S, so that the 
distances AF, AG, shall be equal. 

Solution. Draw the line AK, bisecting the angle BAC (Ge- 
om., B. L, Prop. XL), and through the point S draw GF per- 
pendicular to AK (Geom., B. L, Prop. XIY.), and it will be the 
line required. 

For, comparing the two triangles ALF, ALG, we have the 
angle LAF equal to the angle LAG by construction ; the angle 
ALF equal to the angle ALG, each being a right angle, and the 
side AL common : hence we have two angles and the interja- 
cent side of the one triangle equal to two angles and the inter- 
jacent side of the other ; consequently, the triangles are equal, 
and AF -■= AG (Geom., B. I., Prop. IV.). 





§ 85.] SURVEYING. 141 

PROBLEM II 

Let AB and AC be two roads, and suppose S to he a well of 
water : it is required to pass a new road by $, so that the distance 
SF may equal SC. 

Solution. Through S draw SD par- 
allel to AB ; make DC equal to DA ; 
draw the line CS, and produce it to 
F, and it will be the position of the 
required road (B. IV., Prop. X.). a 

PROBLEM III. 

To find a triangle that shall be equivalent to a gwen polygon. 

Let ABCDF be the given polygon. 
Draw the diagonal CF, cutting off the 
triangle CDF; through the point D 
draw DG parallel to CF, and meeting 
AF produced ; draw CG, and the poly- 
gon ABCDF will be equivalent to ABCG, which has one side 
less than the original polygon. 

For, the triangles CDF, CGF, have the common base CF ; 
and they have the same altitude, since their vertices D and G 
are situated in the line DG, which is parallel to the base CF ; 
therefore these triangles are equivalent (Geom., B. II., Prop. 
II.). To each add the figure ABCF, and we shall have the 
polygon ABCDF equivalent to the polygon ABCG. 

For a similar reason, the triangle CAH may be substituted 
for the equivalent triangle CAB, and thus the pentagon ABCDF 
will be changed into an equivalent triangle HCG. 

It is obvious the same process may be applied to a polygon 
having any number of sides ; each step lessening the number of 
sides by one, until we finally arrive at an equivalent triangle. 

PROBLEM IV. 

To make a polygon similar to a given polygon, and having its 
perimeter in a given ratio to the perimeter of the given polygon. 

Let ABCDF be the given polygon. 

From any point either within or without the polygon, as G, 



142 



SURVEYING. 



[CHAP. XI. 




draw lines to all the angles of the 
polygon. Then take GH, GK, GL, 
GM, GN, each in the same ratio to 
the corresponding lines GA, GB, 
GC. GD, GF, that the perimeter 
of the required polygon is to be to 
the perimeter of the given polygon. 
Join the points H, K, L, M, N, and 
the polygon HKLMN will be the 
polygon required. 

These polygons are evidently 
similar, for the corresponding sides 
are parallel (Geom., B. IY. Prop. 
II.) ; and since in. the triangle 
GAB, HK is parallel to AB, we 
have HK : AB : : GK : GB ; and as the side KL is parallel 
to BC, we have GK : GB : : KL : BC. Therefore, by equal- 
ity of ratios, we have HK : KL : : AB : BC. 

In the same way it may be shown that KL : LM : : BC : CD, 
and so on for the other sides. Therefore these polygons are 
similar. 




PROBLEM V. 



To draw a complex figure similar to another figure, on the 

same or different scales, by means of rectangles. 







^ 


) 






{ 




V 











\ 


-^ 


) 




( 


\ 


^v 


V 





Surround the given figure by a square or a rectangle of con- 
venient size, and divide it by pencil lines, intersecting perpen- 
dicularly, into squares or rectangles, as small as may be deemed 
necessary. Generally, the more irregular the contour of the fig- 
ure, or the more numerous the sinuosities or subdivisions, the 
more numerous the rectangles should be. 

Then draw another square or rectangle, having its sides either 
equal to the former, or greater or less in the assigned ratio, and 



§ 85.] SURVEYING. 143 

divide this figure into as many squares or rectangles as there 
are in the original figure. Draw, in every rectangle of the new 
figure, right lines or curved, to agree with what is contained in 
the corresponding rectangle of the original figure ; and this, if 
carefully done, will give a correct copy of the complex diagram 
proposed. 

In ornamental needle-work, the same system of copying is 
practised. The figures to be executed are usually required to 
be wrought on coarse canvas, the threads of which form a sys- 
tem of squares, such as above described. The original object 
from which the copy is made, is delineated in proper colors on 
paper on which a similar system of squares is printed, the color 
occupying each square being there distinctly expressed ; so that 
the needle-worker sees, at once, what color of silk or worsted it 
is necessary to make use of for each respective square. 

PROBLEM VI 

To determine the difference between the present magnetic me- 
ridian, and the meridian at a time when a tract of land was 
formerly surveyed, so that we may accurately run out the origi- 
nal boundaries. 

Go to any part of the premises, when any two adjacent cor- 
ners are known. 

1. If one of the corners can be seen from the other, take the 
bearing of the side joining these corners, and compare it with 
the bearing of the same line as given in the former survey, and 
we shall thus obtain the difference required. 

2. If one of the corners cannot be seen from the other, then 
run the line according to the given bearing, and measure the 
nearest distance between the line so run and the second corner ; 
then divide this nearest distance by the length of the given line, 
and the quotient will be the sine of the difference sought. 

PROBLEM VII. 

To find the height of a perpendicular object, by means of an 
artificial horizon. 

An artificial horizon is a horizontal surface of any substance 
capable of reflecting light uniformly, as the surface of mercury, 



144: 



SURVEYING-. 



[CHAP. XI. 




ink, etc. If soft treacle be placed in a saucer, it will form a 
very good artificial horizon. 

Place the artificial horizon at 
F, and the eye at D, so that the 
top of the object may be seen by 
reflection in F. Measure the 
height CD of the eye, and the 
distances CF and FA ; then, 
since the triangles FCD and FAB are obviously similar, we 

have 

CF : CD : : FA : AB. 

The perpendicular height of an object maybe found by means 
of its shadow, by placing a stick, of known length, perpendicu- 
larly in the ground, and measuring the length of its shadow : 
then make the following proportion : 

Shadow of the stick : shadow of the object : : height of the stick : height of the object. 

Thales is said to have taught the Egyptians how to measure 
the height of the pyramids, by means of their shadows. 



PROBLEM VIII. 

To find the width of a river without crossing it 

Take a position C in a di- 
rect line with A and B ; also 
take any point, as D, near 
the bank of the river. Then, 
having driven stakes at A, 
C, and D, stretch a line from 
C to A, and thence to D : 
mark that point of the line 
which touches the stake at 
A. Remove the line, and 
exchange ends ; that is, fast- 
en to the stake D the end which was first made fast at C, and 
fasten upon C the end D ; then, taking hold of the line at the 
point which was in contact with A, stretch the line so that it 
shall take the position CFD. The figure ADFC is evidently a 
parallelogram, since, by construction, the opposite sides are 
equal. On the line AD, take the point G in a direct line with 




,n oj.] SURVEYING. 145 

FB. The two triangles FDG and BAG are similar, since the 
angles ABG and DFG are alternate in reference to the parallels 
BC, PF, and are therefore equal (Geom., B. I., Prop. XVII.) ; 
also the angle AGB is equal to FGD, being opposite angles 
(Geometry, B. I., Prop. II.). These two triangles, having equal 
angles, are similar, and we have (Geometry, B. IY., Prop. XI.) 

GD : DF : : GA : AB. 

In this proportion, the first, second, and third terms being 
known, we can find the fourth term, which is the distance sought. 

PROBLEM IX. 

To find a point within a triangle from which the three sides 
shall subtend equal angles. 

Let AB = a; BC=5; AC = c; AP=a?; BP=y; CP=s. 

By the question, we have c 

the angle APB=BPC=CPA 
=120°. 

We find, by Chap. IV., 
Case IV., equation (5), by 
observing that the cosine of 
120° =-i, as follows: 

A 

cos. APB - cos. 120° = - \ = ^-t^-— , . . . (1.) 

cos. BPC=cos. 120°=-i = ^ , . . (2.) 

2 2yz v ' 

. cos. CPA = cos. 120° = - \ = £_2^L_£1 . . (3 .) 

£i ZX 

By clearing of fractions and transposing, these equations read- 
ily become 

x 2 + xy + y*=a? J . . . . (4.) 
tf + yz + J=W, .... (5.) 
z* + zx + x 2 = c 2 , (6.) 

which equations are precisely those given in example 15 of 
Quadratics, page 193 of Treatise on Algebra. The solution is 
there fully wrought out, the result of which is as follows : 

10 




146 



x = 



y = 



z = 



SURVEYING. 

k + cP-V + c 2 
m ' 



[chap. XI. 



where £ = ±\Zf (a 2 & 2 + JV + ^a*)-* (a 4 + & 4 + c% 



m = ± V2 (a 2 + & 2 + c 2 ) + 6 A. 



PROBLEM X. 



From three points in the same horizontal plane, whose dis- 
tances from each other are known, the angles of elevation of the 
summit of a hill or building are observed, from which it is re- 
quired to find its height. 




Denote AB, the height of the object required, by x. Let C, 
D, and E be the points from which the observations were made, 
and put DE = a ; DC = b ; CE = c. Also denote the angle of 
elevation at C by a ; at E by j3 ; at D by y. Then we shall have 
CA = x cotan. a ; EA = x cotan. /3 ; DA = x cotan. y. 

In the triangle CDE we have, Chap. IV., Case IY., equation 
(5), 

oofc CDE = £+|=£, . . . (1.) 



§ 85.] SURVEYING. 147 

The triangle ADE, in a similar manner, gives 

. a 2 + (cotan. 2 y— cotan. 2 (3) x 2 •■ e N 

cos. ADE = *~ '- — , . (2.) 

2 a cotan. y .x J 

Also the triangle ADC gives 

a ^n b 2 + (cotan. 2 r— cotan. 2 a) x 2 , 

cos. ADC = v oA — f — , . (3.) 

2 6 cotan. 7 . x ; y 

But the angle CDE = ADE + ADC ; hence, 

cos. CDE=cos. (ADE+ADC)=cos. ADE cos. ADC 
-sin. ADE sin. ADC. 

If in this last result we substitute ^1 — cos. 2 ADE for sin. ADE, 
and ^1— cos. 2 ADC for sin. ADC, and square the whole so as 
to free it of radicals, we shall find the following expression : 

1 + 2 cos. CDE cos. ADE cos. ADC-cos. 2 CDE-cos. 2 ADE 
-cos. 2 ADC = (4.) 

Substituting in this expression the values given by (1), (2), and 
(3), and putting simply a, /3, y for cotan. a, cotan. /3, cotan. y, 
we obtain, after considerable reduction, 

[a 2 a*+bW+<?y A - e?P(a*W-<?)- a 2 7 2 (« 2 +c 2 -5 2 )-iS 2 7 2 (5 2 +c 2 -a 8 )] 
x^-^^+c 2 -^ 2 ) +6 2 /3 2 (» 2 +c 2 -J 2 )+cy (a 2 +J 2 -c 2 )] . a? 
+aW=0 (5.) 

This being solved by the usual method of quadratics, gives 

where, • "^L-SB"^ ' * * ' W 

A= aV(W-fl«) + £ 3 /3 2 (^H-c 2 - 6 2 )+ cy (^-l-^-c 2 ), 

B = [ (A 2 + 5 2 /3 2 + ^y 2 ) - 4 (a W/3 2 + aWy 2 + &Wy) ] x 

[(^ 2 + 6 2 + c 2 )-4(^ 2 +^ 2 c 2 +5V0 ], 
C= 
aV+5 2 /3 4 +cy- a »j8«(a« + b 2 -<f)-ay (a 2 +c 2 -5 2 ) - £y(P-H*-<A) 

When the three angles of elevation are equal, equation (5) 
immediately gives 



_ ±afo r 



a l2{a 2 b 2 + a 2 <? + b 2 <?)-{a* + V + c*)V ' V ' 
which is readily changed into the following : 

. 1 dw /QX 

x=±- x . ■■ =. (8.) 

« s/(a+b + c)(-a+b + c)(a-b+c){a+b--c) 



148 



SURVEYING, 



[CHAP. XI. 



If we denote the radius of the circle circumscribing the trian- 
gle CDE by E. (see Geometry, Appendix, Prob. IV., equation 
[5J), we shall have 

x = ±- xE=±Ex tangent of the angle of elevation. 

It must be borne in mind that in this solution, as given by 
(6), a, /?, 7, represent the cotangents of the angles of elevation. 

The double sign in the numerator of (6) indicates two different 
positions for the point A of diagram, one without the triangle 
CDE and the other within it. The double sign without the rad- 
ical indicates two inverted symmetrical positions of the point B, 
one above and the other below the horizontal plane of observa- 
tion. 

PROBLEM XL 

From a station P there can he seen three objects, in the same 
horizontal plane, A, B, and 0, whose distances from each other 
are known, viz. AB = 800 = c, AC = 600 = b, and BC = 400 == a. 
The following horizontal angles were taken: APC=33° 45'=m, 
and BPC = 22° 30'=^. It is required tojmd the distances PA, 
PB, and PC. 




GEOMETRICAL SOLUTION. 



On both sides of the line AC, as a chord, describe segments 
of a circle, as APiEP 4 C, AP 3 DP 2 C, capable of containing angles 
equal to 33° 45' (Geometry, B. III., Prop. XV.). 




§ 85.] SURVEYING. 149 

Also on both sides of the line BC, as a chord, describe seg- 
ments, as BPjFPgC, BP 4 GP 2 C, capable of containing angles 
equal to 22° 30'. The points of intersection of the four arcs 
thus described will be the stations sought. 

In general, there will be four points of intersection ; there 
can never be more, but there may be less. In this example 
there are four, so that the problem has four distinct answers. 

TRIGONOMETRICAL SOLUTION. 
CASE I. 

Draw AH and BH meeting at H, so 
that ABH = 33° 45' = m, BAH = 22° 30' 
= n. Then join CH, and produce it 
until it meets the circumference of the 
circle passing through the three points 
A, B, and H, at the point P, which will 
be the point sought. 

For the angle APH is equal to ABH, 
each being measured by half the arc AH 
(Geometry, B. HI., Prop. VII.) ; but the angle ABH was made 
equal to 33° 45' ; hence the angle APC is equal to 33° 45'. In 
a similar way it may be shown that the angle BPC is equal to 
22° 30'. 

If we denote the angle BAC by^>, the triangle ABC will give 
(Chap. IV., Case IV., equation 5) 

C0S ^ = -JFc— ■ ■ ■ (1 > 

By Theorem I., Oblique Trigonometry, the triangle ABH 

gives 

ATT sin. m fn . 

AH = . x c. . . (2.) 

sin. {?n -\-n) x ' 

In the triangle ACH, if we denote half the difference of the 
angles AHC and ACH by £, we shall have, Chap. IV., Case 
ELL, equation (1), 

tan g- 9. = fj^XR x cotan ' * ^" n ^ ' ' ^ 

Since half the sum of these angles is 90°—^ {p—^\ we 
shall have 90°— \ (p—n)—q for the angle ACH, the comple- 



150 



SURVEYING. 



[CHAP. XI. 



ment of which is ^ (p—n) + q ; hence, applying Theorem I. of 
Oblique Trigonometry, to the triangle ACP, we have 



AP = cos -B0?-^) + g] x h 



sin. m 



(*•) 



The remaining three cases, as given below, are readily made 
out from the first, being only modifications of that. 



CASE II. 





cask rv. 




§85.] 



SURVEYING. 



151 



Equations (1), (2), (3), and (4), when modified as below, 
embrace the four solutions. 






AH = 



2 be 

sin. m 



x <?, 



sin. (m ± n) 

h- AH , .. 
tang, q = ^ + AH x cotan. J (p q= n), 

Ap = cos. H (j?Tft)+g] x 5 



sin. m 



(1'0 

(2'.) 

(3'-) 
(4'.) 



Equation (1') remains the same for the four cases. In equa- 
tion (2') the plus sign of n must be used for Cases I. and H., 
and the minus sign lor Cases III. and IV. 

In equations (3') and (4'), the minus sign of n must be used 
for Cases I. and III., and the plus sign for Cases II. and IV". 

After finding AP it will not be difficult to find BP and CP. 

If we apply the foregoing formulas to this example, we shall 
find as follows : 




152 SURVEYING. [CHAP. XI. 

/ AP X = 710-193, 

Case I. } BPi = 934291, 

( CPj = 1042-522. 

(AP 2 = 910-277, 

Case H. ] BP 2 = 764-854, 

( CP 2 = 434-001. 

(AP 3 = 164-319, 

Case III. i BP 3 = 960-528, 

( CP 3 = 729-640, 

/ AP 4 = 981-150, 

Case IV. | BP 4 = 185-540, 

( CP 4 = 565-059. 



PROBLEM XII. 

To divide the triangle ABC into four equal parts ly two 
straight lines DF and EG, which shall he at right angles with 
each other. 

Let 6 represent the angle o 

BAC, and V the angle ABC. 
Also denote the side AB by 
#, and the area of the trian- 
gle by A. The above quan- 
tities are all supposed to be 
known. For unknown quan- 
tities, assume AE=a? ; BD= 
x' ; angle AEG = x ; angle 

BDF = x'- A D 

Twice the area of the triangle AEG is 

x 2 sin. 6 sin. x '__ $ sin. 6 sin. x _ x * _ a 

sin. (& •+■ x) sin. 6 cos. x + cos - ^ sin. x cotan. 0+cotan. x n \ 

Twice the area of the triangle BDF is 

OJ^sinJ'sin-x^ a?' 2 sin. 6* sin.x' _ #' 2 _* 

sin. (d'+x'j ~sinJ'cos.x'+cosJ / sin.x / ~~cotanJ / +cotan.x' ,%{ 




Twice the area of the triangle DEH is 

(x + x'—a) 2 sin. x sin. x' _ ( x + #' — a)* _ A 
sin. (x+xT" ~ cotan. x + cotan. x'~" %' 



(3.) 



§85.] . SURVEYING. 153 

If conditions (1), (2), and (3) are satisfied, the triangle ABC 
will be divided into four equal parts by the two lines DF and 
EG. Now that these two lines may be at right angles with 
each other, we must have 

X + X'=90°,or x '==90°-x. • • (4.) 
Making use of (4) in (2) and (3), we obtain 

x ' 2 -A- (f{\ (% + %' — a) 2 _A . 



cotan. &'-\- tang, x cotan. x + tang, x 2 

. 4 

Equation (1) gives 

A x 2 — A cotan. 6 
tang - * = a?- A cotan. t ; COtan - * = A ' 

These values cause (5) and (6) to become 

-T- = cotan. 6' + -^ — r -, . . ft.) 

A a^-Acotan.d' K J 

2 (x -{- x' — a) 2 __x 2 — A cotan. . A 

A A "^-Acotan.d* ^ 

Equation (7) gives 

x'=± | A cotan. 6'+— — A- 1 * . (9.) 

( af — A cotan. 5 ) v ' 

Substituting this value of x' in (8), we shall have a single 
equation involving only one unknown quantity a?, which may 
then be found. 



TABLE I., 



OF 



LOGARITHMS OF NUMBERS 



FROM 



1 to 10000. 



N. 


Log. 


N. 


Log. 


N. 


Log. 


N. 


Log. 


I 


o- 000000 


26 


I.4I4973 
i-43i364 


5i 


1-707570 


76 


I- 880814 


2 


o-3oio3o 


27 


52 


1 -7i6oo3 


77 


1-886491 


3 


0-477121 


28 


i-447i58 


53- 


1-724276 


78 


1-892095 


4 


o- 602060 


29 


- 1-462398 


54 


1-732394 


79 


1-897627 


5 


0-698970 


3o 


I-477 121 


55 


i«74o363 


80 


1-903090 


6 


0-778151 


3i 


1 -49i362 


56 


i- 7481 88 


81 


I-908485 


7 


0-845098 


32 


1 -5o5i5o 


5 7 


i-7558 7 5 


82 


i-9i38i4 


8 


0-903090 


33 


i-5i85i4 


58 


1-763428 


83 


1-919078 


9 


0-954243 


34 


1 -53 1479 


5 9 


1-770852 


84 


1-924279 


10 


1 -000000 


35 


1.544068 


60 


i-778i5i 


85 


1-929419 


ii 


i-o4i3o3 


36 


i-5563o3 


61 


i-78533o 


86 


1 -934498 


12 


1-079181 


3'7 


1-568202 


62 


1 -792392 


87 


1-939519 


i3 


1 -113943 


38 


1-579784 


63 


1-799341 


88 


1-944483 


14 


1-146128 


3 9 


1-591065 


64 


1-806180 


89 


1 • 949390 


i5 


1-176091 


4o 


1 -602060 


65 


1-812913 


90 


1-954243 


16 


1 -204120 


4i 


1-612784 


66 


1-819544 


9i 


1 -959041 


11 


i-23o449 


42 


1-623249 


67 


1-826075 


92 


1-963788 


1 8 


1-255273 


43 


1-633468 


68 


1-832509 


9 3 


1.968483 


19 


1-278754 


44 


1.643453 


69 


1-838849 


94 


1-973128 


20 


i-3oio3o 


45 


1 .6532i3 


70 


i- 845098 


9 5 


1-977724 


21 


1-322219 


46 


1-662758 


7i 


1 -85i258 


96 


1-982271 


22 


I -34242 6 


47 


1-672098 


72 


i-85 7 333 


97 


1-986772 


23 


1-361728 


48 


1 -681241 


73 


1-863323 


98 


1 -991226 


24 


i-38o2ii 


49 


1 -690196 


74 


1-869232 


99 


1 -995635 


25 


1.397940 


5o 


1 -698970 


7 5 


1 -875061 


100 


2 • 000000 



N". B. In the following table, in the last nine columns of each page, where the 
first or leading figures change from 9's to O's, the character ♦ is introduced instead 
of the O's, to catch the eye, and to indicate that from thence the annexed first 
two figures of the Logarithm in the second column stand in the next lower line, 
directly under the asterisk. 



2 




LOGARITHMS OF NUMBERS. Table I. 


N. 





1 


2 


3 


4 


5 


6 


1 


8 


9 


D. 


100 


00 0000 


0434 


0868 


i3oi 


1734 


2166 


25 9 8 


3029 


346i 


38 9 i 


432 


101 


432i 


4751 


5i8i 


5609 


6o38 


6466 


6894 


7321 


7748 


8174 


428 


102 


*86oo 


9026 


945i 


9876 


♦3oo 


0724 


1 147 


1570 


i 99 3 


24i5 


424 


io3 


01 2837 


3259 


368o 


4100 


452i 


4940 


536o 


5779 


6197 


6616 


419 


104 


#7o33 


745 1 


7868 


8284 


8700 


9116 


9532 


9947 


♦36i 


o 77 5 


416 


io5 


02 1 1 89 


i6o3 


2016 


2428 


2841 


3252 


3664 


4075 


4486 


4896 


412 


106 


53o6 


5715 


6i25 


6533 


6942 


7350 


7757 


8164 


8571 


8978 


408 


107 


*g384 


0789 


♦195 


0600 


1004 


1408 


1812 


2216 


2619 


3021 


404 


108 


o3 3424 


3826 


4227 


4628 


5029 


543o 


583o 


623o 


6629 


7028 


400 


109 


#7426 


7825 


8223 


8620 


9017 


94U 


981 1 


♦207 


0602 


0998 


3 9 6 


no 


04 i3g3 


1787 


2182 


2576 


2969 


3362 


3755 


4i48 


454o 


4932 


3 9 3 


III 


5323 


5714 


6io5 


6495 


6885 


7275 


7664 


8o53 


8442 


883o 


389 


112 


•35-9218 


9606 


9993 


♦38o 


0766 


n53 


i538 


1924 


2309 


2694 


386 


n3 


o5 3078 


3463 


3846 


423o 


46i3 


4996 


53 7 8 


5760 


6142 


6524 


382 


114 


45-6905 


7286 


7666 


8046 


8426 


88o5 


9i85 


9 563 


9942 


♦320 


3 79 


n5 


06 0698 


1075 


i452 


1829 


2206 


2582 


2958 


3333 


3709 


4o83 


376 


116 


4458 


4832 


5206 


558o 


5953 


6326 


6699 


7071 


7443 


7815 


372 


117 


*8i86 


8557 


8928 


9298 


9668 


♦o38 


0407 


0776 


ii45 


i5i4 


36 9 


118 


07 1882 


2250 


2617 


2 9 85 


3352 


3 7 i8 


4o85 


445 1 


4816 


5i82 


366 


119 


5547 


5912 


6276 


6640 


7004 


7368 


7731 ' 


8094 


8457 


8819 


363 


120 


*9i8i 


9543 


9904 


♦266 


0626 


0987 


1 347 


1707 


2067 


2426 


36o 


121 


08 2785 


3i44 


35o3 


386i 


4219 


4376 


4934 


5291 


5647 


6004 


357 


122 


636o 


6716 


7071 


7426 


7781 


8i36 


8490 


8845 


9198 


9552 


355 


123 


*99o5 


♦258 


061 1 


0963 


i3i5 


1667 


2018 


2370 


2721 


3071 


35i 


124 


093422 


3 77 2 


4122 


4471 


4820 


5169 


55i8 


5866 


62i5 


6562 


349 


125 


■^■6910 


7 25 7 


7604 


7 9 5i 


8298 


8644 


8990 


9 335 


9681 


♦026 


346 


126 


10 0371 


0715 


1059 


i4o3 


1747 


2091 


2434 


2777 


3i 19 


3462 


343 


127 


38o4 


4i46 


4487 


4828 


5169 


55io 


585i 


6191 


653 1 


6871 


34o 


128 


* 7210 


7549 


7888 


8227 


8565 


8 9 o3 


9241 


9579 


9916 


♦253 


338 


129 


1 1 0590 


0926 


1263 


1 5 99 


1934 


2270 


26o5 


2940 


3275 


3609 


335 


i3o 


3 9 43 


4277 


461 1 


4944 


5278 


56n 


5 9 43 


6276 


6608 


6940 


333 


i3i 


* 7271 


7603 


79 34 


8265 


85 9 5 


8926 


9256 


9 586 


9915 


♦245 


33o 


l32 


12 0574 


0903 


I23l 


i56o 


1888 


2216 


2344 


2871 


3i 9 8 


3525 


328 


i33 


3852 


4178 


45o4 


483o 


5i56 


5481 


58o6 


6i3i 


6456 


6781 


325 


i34 


* 7105 


7429 


7753 


8076 


8399 


8722 


qo45 


9 368 


9690 


♦012 


323 


i35 


i3 o334 


o655 


0977 


1298 


1619 


1939 


2260 


258o 


2900 


3219 


321 


i36 


353 9 


3858 


4i77 


4496 


4814 


5i33 


545 1 


5769 


6086 


64o3 


3i8 


i3 7 


6721 


7037 


7354 


7671 


7987 


83o3 


8618 


8 9 34 


9249 


9564 


3i5 


i38 


*9 8 79 


♦ 194 


o5o8 


0822 


n36 


i45o 


1763 


2076 


238 9 


2702 


3i4 


139 


i4 3oi5 


3327 


363 9 


3951 


4263 


4574 


4885 


5196 


5507 


58i8 


3u 


140 


6128 


6438 


6748 


7o58 


7367 


7676 


79 85 


8294 


86o3 


8911 


309 


141 


*92I9 


9527 


9 835 


♦142 


0449 


0756 


io63 


1370 


1676 


1982 


307 


142 


i5 2288 


2594 


2900 


32o5 


35io 


38i5 


4120 


4424 


4728 


5o32 


3o5 


143 


5336 


564o 


5q43 


6246 


6549 


6852 


7i54 


7457 


77 5 9 


8061 


3o3 


144 


* 8362 


8664 


8 9 65 


9266 


9 56 7 


9868 


♦168 


0469 


0769 


1068 


3oi 


145 


16 i368 


1667 


1967 


2266 


2564 


2863 


3i6i 


3460 


3 7 58 


4o55 


299 


146 


4353 


465o 


4947 


5244 


554i 


5838 


6i34 


643o 


6726 


7022 


297 


147 


7317 


7613 


7908 


82o3 


8497 


8792 


9086 


9 38o 


9674 


9968 


295 


148 


17 0262 


o555 


0848 


1 141 


1434 


1726 


2019 


23ll 


26o3 


28 9 5 


293 


149 


3i86 


3478 


3769 


4060 


43 5 1 


4641 


4932 


5222 


55i2 


58o2 


291 


i5o 


6091 


638i 


6670 


6o5 9 


7248 


7536 


7825 


8n3 


8401 


8689 


289 


i5i 


« 8 F 


9264 


9552 


9 83 9 


♦126 


o4i3 


0699 


0985 


1272 


i558 


287 


l52 


18 1844 


2129 


24i5 


2700 


2985 


3270 


3555 


383 9 


4123 


4407 


285 


1 53 


4691 


4975 


5259 


5542 


5825 


6108 


6391 


6674 


6 9 56 


7239 


283 


1 54 


■x- 7521 


7803 


8084 


8366 


8647 


8928 


9209 


9490 


9771 


♦o5i 


281 


i55 


19 o332 


0612 


0892 


1 171 


i45i 


1730 


2010 


2289 


2567 


2846 


279 


1 56 


3i25 


34o3 


368i 


3959 


423 7 


45i4 


4792 


5069 


5346 


5623 


278 


1 57 


5900 


6176 


6453 


6729 


7oo5 


7281 


7556 


7832 


8107 


8382 


276 


i58 


* 8657 


8 9 32 


9206 


948i 


97 55 


♦029 


o3o3 


0577 


o85o 


1 1 24 


274 


159 


20 1397 


1670 


1943 


2216 


2488 


2761 


3o33 


33o5 


3577 3848 


272 


N. 





1 


2 


3 


4 


5 


6 


7 


8 | 9 | D. 

1 1 














Table I. 


LOGARITHMS OF NUMBERS. 3 


ST. 





1 


2 


3 


4 


5 


6 


n 


8 


9 


D. 


1 60 


204120 


43 9 i 


4663 


4934 


5204 


5475 


5746 


6016 


6286 


6556 


271 


161 


6826 


7090 


7365 


7634 


7904 


8173 


8441 


8710 


8979 


9247 


269 


162 


#95i5 


9783 


♦o5i 


0319 


o586 


o853 


1121 


i388 


i654 


1921 


267 


i63 


21 2188 


2454 


2720 


2986 


3252 


35i8 


3 7 83 


4049 


43i4 


4579 


260 


164 


4844 


5iog 


5373 


5638 


5902 


6166 


643o 


6694 


6957 


7221 


264 


i65 


7484 


7747 


8010 


8273 


8536 


8798 


9060 


9323 


9 585 


98^ 


262 


166 


22 0108 


0370 


o63i 


0892 


n53 


1414 


1675 


i 9 36 


2196 


2^56 


261 


167 


2716 


2976 


3236 


3496 


3 7 55 


401 5 


4274 


4533 


4792 


5o5i 


259 


168 


5309 


5568 


5826 


6084 


6342 


6600 


6858 


71 15 


7 3 Io 


763o 


258 


169 


45-7887 


8i44 


8400 


8657 


8 9 i3 


9170 


9426 


9682 


90J8 


♦193 


256 


170 


23 0449 


0704 


0960 


I2l5 


1470 


1724 


1979 


2234 


2488 


2742 


254 


171 


2996 


3230 


35o4 


3 7 5 7 


401 1 


4264 


4517 


47^ 


5o23 


5276 


253 


172 


5528 


578l 


6o33 


6285 


6537 


6789 


7041 


7 n r 9 2 


7544 


77 9 5 


252 


i 7 3 


*8o46 


8297 


8548 


8799 


9049 


9299 


955o 


9000 


♦o5o 


o3oo 


25o 


174 


24 0549 


0799 


1048 


1297 


i546 


1795 


204' 


2293 


254i 


2790 


249 


i 7 5 


3o38 


3286 


3534 


3782 


4o3o 


4277 


Ji25 


4772 


5019 


5266 


248 


176 


55i3 


5 7 5 9 


6006 


6252 


6499 


. M 5 


0991 


7237 


7482 


7728 


246 


177 


*7973 


8219 


8464 


8709 


8954 


919P 


9443 


9687 


9932 


♦176 


245 


178 


25 0420 


0664 


0908 


ii5i 


1395 


16& 


1881 


2125 


2368 


2610 


243 


*79 


2853 


3og6 


3338 


358o 


3822 


/064 


43o6 


4548 


4790 


5o3i 


242 


180 


5273 


55i4 


5755 


5996 


6237 


6477 


6718 


6 9 58 


7198 


7439 


241 


181 


7679 


7918 


8108 


83 9 8 


8637 


8877 


9116 


9355 


9 5 94 


9 833 


239 


182 


26 0071 


o3io 


o548 


0787 


102? 


1263 


i5oi 


1739 


1976 


2214 


238 


1 83 


245 1 


2688 


2925 


3i62 


33?9 


3636 


3873 


4109 


4346 


4582 


237 


184 


4818 


5o54 


5290 


5525 


5761 


5996 


6232 


6467 


6702 


6 9 3 7 


235 


i85 


7172 


7406 


7641 


787D, 


8110 


8344 


85 7 8 


8812 


9046 


9279 


234 


186 


*95i3 


9746 


9980 


♦21-'' 


0446 


0679 


0912 


1 144 


1377 


1609 


233 


187 


27 1842 


2074 


23o6 


2 ^8 


2770 


3ooi 


3233 


3464 


36 9 6 


3 9 2 7 


232 


188 


4i58 


438 9 


4620 


+ 85o 


5o8i 


53n 


5542 


5 77 2 


6002 


6232 


23o 


189 


. 6462 


6692 


6921 


7i5i 


738o 


7609 


7838 


8067 


8296 


8525 


229 


190 


*8 7 54 


8982 


9 ? An 


9439 


9667 


9895 


♦ 123 


o35i 


0578 


0806 


228 


191 


28 io33 


1261 


t488 


1713 


1942 


2169 


2396 


2622 


2849 


3075 


227 


192 


33oi 


3527 


3753 


3979 


42o5 


443 1 


4656 


4882 


5107 


5332 


226 


193 


5557 


5^8? 


6007 


6232 


6456 


6681 


6905 


7i3o 


7354 


7 5 7 8 


225 


i 9 4 


7802 


8or° 


8249 


8473 


8696 


8920 


9i43 


9 366 


9 58 9 


9812 


223 


i 9 5 


29 oo35 


c257 


0480 


0702 


0925 


1 147 


1369 


1 59 1 


i8i3 


2o34 


222 


196 


2256 


2478 


2699 


2920 


3i4i 


3363 


3584 


38o4 


4025 


4246 


221 


197 


4466 


4687 


4907 


5127 


5347 


5567 


5787 


6007 


6226 


6446 


220 


198 


666'' 


6884 


7104 


7-323 


7542 


7761 


7979 


8198 


8416 


8635 


219 


199 


*88>3 


9071 


9289 


9^°7 


9725 


9943 


♦161 


0378 


0595 


o8i3 


218 


200 


3oio3o 


1247 


1464 


1681 


1898 


2114 


233i 


2547 


2764 


29S0 


217 


201 


3196 


3412 


3628 


3844 


4009 


4275 


4491 


4706 


4921 


5i36 


2l6 


202 


535i 


5566 


5 7 8i 


0996 


6211 


6425 


663 9 


6854 


7068 


7282 


2l5 


203 


7496 


7710 


7924 


8137 


835i 


8564 


8778 


8991 


9204 


94i7 


2l3 


20^ 


* 9630 


9843 


•*o56 


0268 


0481 


0693 


0906 


1118 


i33o 


1 542 


212 


2J3 


3i 1754 


1966 


2177 


238 9 


2600 


2812 


3o23 


3234 


3445 


3656 


211 


206 


386 7 


4078 


4289 


4499 


4710 


4920 


5i3o 


534o 


555i 


5760 


2IO 


207 


5970 


6180 


6390 


6599 


6809 


7018 


7227 


7436 


7646 


7854 


209 


208 


8o63 


8272 


8481 


8689 


8898 


9106 


9314 


9522 


97 3o 


99 38 


208 


209 


32 0146 


o354 


o562 


0769 


0977 


1 184 


1391 


1 5 9 8 


i8o5 


2012 


207 


210 


2219 


2426 


2633 


2839 


3o46 


3252 


3458 


3665 


38 7 i 


4077 


206 


211 


4282 


4488 


4694 


4899 


5io5 


53io 


55i6 


5721 


5926 


6i3i 2o5 


212 


6336 


654i 


6745 


6900 


7 i55 


735o 


7563 


7767 


7972 


8176 


204 


2l3 


*838o 


8583 


8787 


8991 


9194 


9 3 9 8 


9601 


9805 


♦008 


0211 


203 


214 


33 0414 


0617 


0819 


1022 


1225 


1427 


i63o 


i832 


2o34 


2236 


202 


2l5 


2438 


2640 


2842 


3o44 


3246 


3447 


3649 


385o 


4o5i 


4253 


202 


2l6 


4454 


4655 


4856 


5o57 


5257 


5458 


5658 


585 9 


6o5 g 


6260 


201 


217 


6460 


6660 


6860 7060 


7260 


7459 


765 9 


7858 


8o58 


8257 


200 


2l8 


* 8456 


8656 


8855 


9054 


9253 


945 1 


9650 


9849 


♦047 


0246 


I90 


219 


34 0444 


0642 


0841 


1039 


1237 


i435 


i632 


i83o 


2028 


2225 


I98 

D. 


N. 


0, 


1 


2 


3 


4 


5 


6 i 


8 


9 



LOGARITHMS OF NUMBERS. 



Table I. j 



N. 

220 
221 
222 
2i3 
224 

225 
226 
227 
228 
229 

23o 

23 1 
232 

233 
234 

235 

236 
237 
238 
239 

240 
241 
242 
243 

244 

245 

246 
247 
248 
249 

25o 

25l 
252 

253 
254 

255 
256 
257 
258 
259 

260 
261 
262 
263 
264 

265 
266 
267 
268 
269 

270 

271 
272 
273 
274 

273 
276 
277 
278 
279 

N. 







34 2423 
4392 
6353 

*83o5 

35 0248 

2i83 
4108 
6026 

79^ 
*9o35 

361728 

36i2 

5488 

7356 

#9216 

37 1068 
2912 

4748 

65 7 7 

*83g8 

38o2ii 
2017 
38i5 
56o6 
7390 

*9i66 

39 0935 
2697 
4452 
6199 

7940 
#9674 

40 1401 

3l2I 

4834 

654o 
8240 

* 9933 

41 1620 
33oo 

4973 
6641 
83oi 

* 9956 

42 1604 

3246 

4882 

65n 

8i35 

*9752 

43 1 364 
2969 
456 9 
6i63 
775i 

* 9333 
440909 

2480 
4o45 
56o4 





2620 
4589 
6549 
85oo 
0442 

2375 
43oi 
6217 
8i25 

♦025 

38i\o 
5675 
7542 
9401 

1253 
3096 
4932 
6759 
858o 

0392 

2197 
3 9 o5 

5785 
7 568 

9343 
1112 

2873 
4627 
6374 

8114 

9847 
1573 
3292 
5oo5 

6710 
8410 

♦ 102 
1788 
3467 

5i4o 
6807 
8467 

♦ 121 
1768 

34io 
5o45 
6674 
8297 
9914 

i525 
3i3o 

4729 

6322 

7909 
9491 

1066 
2637 
4201 
5760 



2817 

4785 
6744 



o636 

2568 
4493 
6408 
83i6 

02l5 

2io5 

3988 

5862 
T729 
9^7 
1437 
3280 
5n5 
6942 
8761 

0573 
23 77 
4174 
5964 
7746 

9520 
1288 
3o48 
4802 
6548 

8287 
♦020 
1745 
3464 
5176 

6881 

8579 
0271 
19% 
3635 

53o7 
6973 
8633 
0286 
1933 

35 7 4 
52o8 
6836 
845o 
♦075 

i685 
3290 
4888 
6481 
8067 

9648 
1224 
2 7 o3 
435 7 
5915 



3oi4 

4981 
6 9 3 9 
8889 
0829 

2761 
4685 
6599 
85o6 
0404 

2294 
4176 
6049 
791D 
9772 
1622 
^64 
52^8 
7124 
8943 

0754 
2557 
4353 
6142 
7923 



3212 

5178 
7135 
9083 
1023 

2o54 
4876 
6790 



1464 
3224 

4977 
6722 

8461 
0192 
1917 
3635 
5346 

7o5i 

8749 
0440 
2124 
38o3 

5474 
7139 

8798 
045 1 
2097 

3737 
5371 
6999 
8621 
0236 

1846 
345o 
5o48 
6640 
8226 

r«o6 
i38i 
2o5o 
45i3 
6071 



0593 

2482 
4363 
6236 
8101 
9958 

1806 
3647 
5481 
73o6 
9124 

27>> 

4533 

632i 
8101 

9875 
1641 
34oo 
5i52 
6896 

8634 
o365 
2089 
3807 
55i7 

7221 
8918 
0609 
2293 
3970 

564i 
73o6 
8964 
0616 
2261 

3901 
5534 
7161 
8 7 83 
o3 9 8 

2007 
36io 
5207 
6799 
8384 

99 6 4 
1 538 
3io6 
4669 
6226 



3409 
53 7 4 
733o 
9278 
1216 

3 147 

5o68 
6981 
8886 
0783 

2671 
455i 
6423 
8287 
♦U3 

1991 
383i 
5664 
7488 
93o6 

iii5 

2917 
4712 
6499 
8279 

♦t-5 1 

181, 
35 7 5 
53 2 6 
7071 



o538 
2261 

3978 
5688 

7391 
9087 
0777 
2461 
4i3 7 

58o8 
7472 
9129 
0781 
2426 

4o65 
56 97 
7324 
8944 
0559 

2167 
3770 
5367 
6 9 5 7 
8542 

♦122 
1695 
3263 
4825 
6382 



36o6 
5570 
7525 

9472 
1410 

333 9 
5260 
7172 
9076 
0972 

285 9 

4739 
6610 
8473 
o328 

2175 
4oi5 
5846 
7670 
9487 

1296 
3o 97 
4891 
6677 
8456 

0228 
1993 
3 7 5i 
^5oi 
7H5 

8981 
07 1 1 
2433 
4149 
5858 

756i 
9257 
0946 
2629 
43o5 

5974 
7638 
9295 
0945 
2590 

4228 
586o 
7486 
9106 
0720 

2328 

3930 

5526 

7116 
8701 

0279 
i852 
3419 
4981 
653 7 



38o2 
5766 
7720 
9666 
i6o3 

3532 
5452 
7363 
9266 
1161 

3o48 
4926 
6796 
865o 
o5i3 

236o 
4198 
6029 

7852 



8 



U76 
3277 
5070 
6856 
8634 

o4o5 
2169 
3926 
56 7 6 
74i9 

9154 

o883 
*6o5 
4ooo 
602^ 

773 1 
9426 
1114 
2796 
4472 

6141 

7804 
9460 
mo 
2754 

4392 
6023 
7648 
9268 
0881 

2488 
4090 
5685 
7275 
885 9 

0437 
2009 
3576 
5i3 7 
6692 



3.999 
5962 
7 9 i5 
9860 
1796 

3724 
5643 
7554 
9456 
i35o 

3236 
5n3 

6 9 83 
8845 
0698 

2544 
4382 
6212 
8o34 
9849 

i656 
3456 
5249 
7034 
881 1 

o582 
2345 
41 01 
585o 
7592 

9328 
io56 

2777 
4492 
6199 

7901 
95o5 
12I3 
2962, 
4639 

63o8 
7970 
9625 
1275 
2918 

4555 
6186 
7811 
9429 
1042 

2649 
4249 
5844 
7433 
9017 

0594 
2166 
3732 
5293 
6848 



4196 
61D7 
8110 
♦o54 
1989 

3916 
5834 
7744 
9646 
1539 

3424 
53oi 
7169 
9o3o 
o883 

2728 
4565 
6394 
8216 
♦o3o 

1837 
3636 
5428 
7212 
8989 

0759 

2521 
4277 
6025 
7766 

95oi 
1228 
2949 

4663 
6370 

8070 
9764 
i45i 
3i32 
4806 

<*74 
8115 
9791 
1439 
3o82 

4718 
6349 
7973 
9 5 9 i 

1203 

2809 
4409 
6004 
7592 

9175 

0752 

2323 

3889 
5449 

7003 





Table I. 


LOGARITHMS OF NUMBERS. 


5 


1 

1 


N. 
280 





1 


2 


3 


4 


5 


6 


1 


8 


9 


D. 




44 7i58 


73i3 


7468 


7623 


7778 


7933 


8088 


8242 


83 9 7 


8552 


1 55 




281 


45-8706 


8861 


90i5 


9170 


9 324 


9478 


9 633 


9787 


9941 


♦095 


1 54 




282 


45 0249 


o4o3 


o557 


07 1 1 


o865 


1018 


1 172 


i326 


i479 


i633 


1 54 




283 


1786 


1940 


2093 


2247 


2400 


2553 


2706 


285 9 


3oi2 


3i65 


1 53 




284 


33i8 


3471 


3624 


3777 


3930 


4082 


4235 


438 7 


4540 


4692 


1 53 




285 


4845 


4997 


5i5o 


53o2 


5454 


56o6 


5 7 58 


5910 


6062 


6214 


152 


1 


286 


6366 


65i8 


6670 


6821 


6973 


7125 


7276 


7428 


7579 


7731 


152 




287 


7882 


8o33 


8184 


8336 


8487 


8638 


8789 


8940 


9091 


9242 


i5i 


1 


288 


: -*93g2 


9 543 


9694 


9845 


999 5 


♦ 146 


0296 


0447 


0597 


0748 


i5i 


1 


289 


46 0898 


1048 


1198 


1 348 


U99 


1649 


1799 


1948 


2098 


2248 


i5o 




290 


2398 


2548 


2697 


2847 


2997 


3 146 


3296 


3445 


35 9 4 


3744 


i5o 




291 


38 9 3 


4042 


4191 


4340 


4490 


463g 


4788 


4936 


5o85 


5234 


149 




292 


5383 


5532 


568o 


5829 


5977 


6126 


6274 


6423 


65 7 i 


6719 


1 49 




293 


6868 


7016 


7164 


73i2 


7460 


7608 


77 56 


7904 


8o52 


8200 


148 




294 


8347 


8495 


8643 


8790 


8 9 38 


9 o85 


9233 


938o 


9527 


9675 


148 




295 


#9822 


9969 


♦116 


0263 


0410 


o557 


0704 


o85i 


0998 


1 U5 


147 




296 


47 1292 


143^8 


1 585 


1732 


1878 


2025 


2171 


23i8 


2464 


2610 


146 


'■'■ 


297 


2706 


2903 


3o49 


3195 


334i 


3487 


3633 


3779 


3925 


4071 


146 




298 


4216 


4362 


45o8 


4653 


4799 


4944 


5090 


5235 


538i 


5526 


146 




299 


5671 


58i6 


5962 


6107 


6252 


63 97 


6542 


6687 


6832 


6976 


145 




3oo 


7121 


7266 


741 1 


7555 


7700 


7844 


7989 


8i33 


8278 


8422 


145 


1 


3oi 


8566 


8711 


8855 


8999 


9143 


9287 


9 43 1 


9575 


9719 


9 863 


144 


' 


3o2 


48 0007 


oi5i 


0294 


0438 


o582 


0725 


0869 


1012 


u56 


1299 


144 




3o3 


1443 


1 586 


1729 


1872 


2016 


2i5g 


2302 


2445 


2588 


2731 


143 


\ 


3o4 


2874 


3oi6 


3 1 59 


33o2 


3445 


3587 


3730 


3872 


401 5 


4i57 


143 


,; 


3o5 


43oo 


4442 


4585 


4727 


4869 


5on 


5i53 


5295 


5437 


5579 


142 




3o6 


5721 


5863 


6oo5 


6147 


6289 


643o 


6572 


6714 


6855 


6997 


142 




307 


7 i38 


7280 


742i 


7563 


7704 


7845 


7986 


8127 


8269 


8410 


Ui 




3o8i 


855i 


8692 


8833 


8974 


9114 


9255 


9396 


9537 


9677 


9818 


141 


: 


309 


* 9958 


♦099 


0239 


o38o 


o520 


0661 


0801 


0941 


1081 


1222 


140 


1 


3io 


49 1 362 


i5o2 


1642 


1782 


1922 


2062 


2201 


234i 


2481 


2621 


140 




3n 


2760 


2900 


3 040 


3i 79 


33 19 


3458 


3597 


3737 


3876 


401 5 


i3 9 


1 


3l2 


4i55 


4294 


4433 


4572 


471 1 


485o 


4989 


5i28 


5267 


5406 


i3 9 




3i3 


5544 


5683 


5822 


5o6o 


6099 

7483 


6238 


6376 


65i5 


6653 


6791 


1 3 9 




3i4 


6930 


7068 


7206 


7344 


7621 


77 5 9 


7897 


8o35 


8173 


i38 




3i5 


83u 


8448 


8586 


8724 


8862 


8999 


9137 


9275 


9412 


955o 


i38 




3i6 


#9687 


9824 


9962 


♦099 


0236 


0374 


o5n 


0648 


0785 


0922 


i3 7 




3i7 


5o 1059 


1 196 


i333 


U70 


1607 


1744 


1880 


2017 


2 1 54 


2291 


i3 7 




3i8 


2427 


2564 


2700 


2837 


2973 


3109 


3246 


3382 


35i8 


3655 


i36 


I 


319 


3 79 i 


3927 


4o63 


4199 


4335 


4471 


4607 


4743 


4878 


5oi4 


i36 


i 


320 


5i5o 


5286 


5421 


555 7 


5693 


5828 


5964 


6099 


6234 


6370 


1 36 




321 


65o5 


6640 


6776 


691 1 


7046 


7181 


73 16 


745 1 


7586 


7721 


i35 




322 


7856 


7991 


8126 


8260 


83 9 5 


853o 


8664 


8799 


8 9 34 


9068 


i35 




323 


*92o3 


9 33 7 


9 ^\ 


9606 


9740 


9874 


♦009 


oi43 


0277 


041 1 


1 34 




324 


5i o545 


0679 


o8i3 


0947 


1 08 1 


I2l5 


i349 


1482 


1616 


1750 


1 34 




325 


1 883 


2017 


2l5l 


2284 


2418 


255i 


2684 


2818 


2951 


3o84 


i33 




326 


32i8 


335i 


3484 


36i 7 


3750 


3883 


4oj6 


4149 


4282 


44i4 


i33 




327 


4548 


4681 


48i3 


4946 


5079 


5s 1 1 


5344 


5476 


5609 


5741 


i33 




328 


58 7 4 


6006 


6139 


6271 


'64o3 


6535 


6668 


6800 


6932 


7064 


l32 




329 


7196 


7328 


7460 


7592 


7724 


7 855 


7987 


8119 


825i 


8382 


l32 




33o 


85i4 


8646 


8777 


8909 


9040 


9171 


93oS 


9434 


9 566 


9697 


i3i 




33i 


4*9828 


99 5 9 


♦090 


0221 


o353 


0484 


o6i5 


0745 


0876 


1007 


i3i 




332 


52 n38 


1269 


1400 


i53o 


1661 


1792 


1922 


2o53 


2i83 


23i4 


i3i 




333 


2444 


2576 


2705 


2835 


2966 


3096 


3226 


3356 


3486 


36i6 


i3o 




334 


3746 


3876 


4006 


4i36 


4266 


4396 


4526 


4656 


4785 


49i5 


i3o 




335 


5o45 


5i74 


53o4 


5434 


5563 


56o3 


5822 


5951 


6081 


6210 


129 




336 


-633 9 


6469 


65 9 8 


6727 


6856 


6 9 85 


7114 


7243 


7372 


75oi 


129 




337 


763o 


7759 


7888 


8016 


8i45 


8274 


8402 


853 1 


8660 


8788 


129 




338 


* 8917 


9045 


9174 


9302 


943o 


9559 


9687 


9 8i5 


9943 


♦072 


128 




339 


53 0200 


o328 


0456 


M 


o584 


0712 


0840 


0968 


1096 


1223 


i35i 


128 




I 





1 


3 


4 


5 


6 


1 


8 


9 


D. 



6 






LOGARITHMS OF NUMBERS 






Table I. j 


N. 





1 


2 


3 


4 


5 


6 


1 


8 


9 


D - 


340 


53 1479 


1607 


1734 


1862 


1990 


2117 


2245 


2372 | 25oo 


2627 


128 I 


34i 


2754 


2882 


3009 


3i36 


3264 


33 9 i 35i8 


3645 3772 


38 99 


127 I 


342 


4026 


41 53 


4280 


4407 


4534 


4661 4787 


4914 5 04 1 


5167 


127 a 


343 


5294 


5421 


5547 


56 7 4 


58oo 


5927 6o53 


6180 | 63o6 


6432 


126 1 


344 


6558 


6685 


6811 


6937 


7063 


7189 73i5 


744i 


7567 


7693 


126 


345 
346 


7819 


7945 


8071 


8197 


8322 


8448 


85 7 4 


8699 


88 2 5 


8 9 5 1 


126. 


4^9076 


9202 


9327 


9432 


9578 


9703 


9829 


9954 


♦079 


0204 


125 


347 


540329 


0455 


o58o 


0705 


o83o 


0955 


1080 


I2o5 


i33o 


1454 


12a 


348 


1 5 7 o 


1704 


1829 


1953 


2078 


2203 


2327 


2452 


2576 


2701 


125 


349 


2825 


2950 


3074 


3199 


3323 


3447 


3571 


36 9 6 


3820 


3944 


124 


35o 


4068 


4192 


43 16 


4440 


4564 


4688 


4812 


4936 


5o6o 


5i83 


124 1 


35i 


53o7 


54 5 1 


5555 


5678 


58o2 


5925 


6049 


6172 


6296 


6419 


124 


352 


6543 


6666 


6789 


6913 


7o36 


71D9 


7282 


74o5 


7529 


7652 


123 


353 


7775 


7898 


8021 


8i44 


8267 


838 9 


85i2 


8635 


8758 


8881 


123 


354 


* 9003 


9126 


9249 


9 3 7 i 


9494 


9616 


97 3 9 


9861 


9984 


♦106 


123 


355 


55o228 


o35i 


o473 


0595 


0717 


0840 


0962 


1084 


1206 


i328 


122 


356 


i45o 


1572 


1694 


1816 


1938 


2060 


2181 


23o3 


2425 


2547 


122 


357 


2668 


2790 


2911 


3o33 


3i55 


3276 


33 9 8 


35i9 


364o 


3762 


121 


358 


3883 


4004 


4126 


4247 


4368 


4489 


4610 


473i 


4852 


4973 


121 


35 9 


5094 


32l5 


5336 


5457 


5578 


5699 


5820 


5940 


6061 


6182 


121 


36o 


63o3 


6423 


6544 


6664 


6785 


6905 


7026 


7146 


7267 


7 38 7 


120 


36i 


7507 


7627 


7748 


7868 


7988 


8108 


8228 


8349 


8469 


8589 


120 . 


362 


8709 


8829 


8948 


9068 


9188 


9308 


9428 


9 548 


9667 


9787 


120 


363 


•x-9907 


♦026 


0146 


0265 


o385 


o5o4 


0624 


0743 


o863 


0982 


II9 


364 


56 1101 


1221 


1 34o 


U59 


i5 7 8 


1698 


1817 


1936 


2o55 


2174 


119 


365 


2293 


2412 


253i 


265o 


2769 


2887 


3oo6 


3 1 25 


3244 


3362 


II9 


366 


348i 


36oo 


3 7 i8 


3837 


3955 


4074 


4192 


43u 


4429 


4548 


"2 


367 


4666 


4784 


4903 


5021 


5i3g 


5257 


5376 


5494 


56i2 


5730 


Il8 


368 


5848 


5 9 66 


6084 


6202 


6320 


6437 


6555 


6673 


6791 


6909 


Il8 


36 9 


7026 


7144 


7262 


7379 


7497 


7614 


77 32 


7849 


7967 


8084 


Il8 


370 


8202 


83 19 


8436 


8554 


8671 


8788 


8 9 o5 


9023 


9140 


9257 


117 


3 7 i 


*9 3 74 


9491 


9608 


9725 


9842 


99 5 9 


♦076 


0193 


o3»9 


0426 


117 


372 


57 o543 


0660 


0776 


o8 9 3 


IOIO 


1 1 26 


1243 


1359 


1476 


i5o2 


117 


373 


1709 


1825 


1942 


2o58 


2174 


2291 


2407 


2523 


2639 


2755 


Il6 


374 


2872 


2988 


3io4 


3220 


3336 


3452 


3568 


3684 


38oo 


3915 


Il6 


375 


4o3i 


4U7 


4263 


4379 


4494 


4610 


4726 


4841 


4957 


5072 


Il6 


376 


5i88 


53o3 


5419 


5534 


565o 


5765 


588o 


5996 


61 1 1 


6226 


n5 


377 


634i 


6457 


6572 


6687 


6802 


6917 


7032 


7i47 


7262 


7377 


n5 


378 


7492 


7607 


7722 


7836 


7g5i 


8066 


8181 


8295 


8410 


8525 


u5 


3 79 


863 9 


8754 


8868 


8 9 83 


9097 


9212 


9326 


944i 


9 555 


9669 


114 


38o 


#9784 


9898 


♦012 


0126 


0241 


o355 


0469 


o583 


0697 


081 1 


114 


38i 


58 0925 


1039 


n53 


1267 


i38i 


i495 


1608 


1722 


i836 


1950 


114 


382 


2o63 


2177 


2291 


2404 


25i8 


263s 


2745 


2858 


2972 


3o85 


114 


383 


3199 


33 1 2 


3426 


3539 


3652 


3765 


38 79 


3992 


4io5 


4218 


u3 


384 


433 1 


4444 


4557 


4670 


4783 


4896 


5009 


5l22" 


5235 


5348 


n3 


385 


5461 


5574 


5686 


5 799 


5912 


6024 


6i3 7 


625o 


6362 


6475 


n3 


386 


6587 


6700 


6812 


6925 


7037 


7149 


7262 


7374 


7486 


7 5 Q9 


112 


387 


7711 


7823 


7 9 35 


8047 


8160 


8272 


8384 


8496 


8608 


8720 


112 


388 


8832 


8944 


9o56 


9167 


9279 


9391 


95 o3 


9615 


9726 


9 838 


112 


389 


*995o 


♦061 


0173 


0284 


0396 


0507 


0619 


0730 


0842 


0953 


112 


390 


59 io65 


1 176 


12*7 


i3 99 


i5io 


1621 


1732 


1843 


1955 


2066 


in 


391 


2177 
3286 


2288 


2399 


25l0 


2621 


2732 


2843 


2954 


3 064 


3i 7 5 


in 


392 


33 9 7 


35o8 


36i8 


3729 


384o 


3g5o 


4061 


4171 


4282 


in 


393 


4393 


45o3 


4614 


4724 


4834 


4945 


5o55 


5i65 


5276 


5386 


no 


3 9 4 


5496 


56o6 


5717 


5827 


5 9 3 7 


6047 


6157 


6267 


63 77 


6487 


no 


3 9 5 


65 9 7 


6707 


6817 


6927 


7037 


7U6 


7256 


I 366 


7476 


7 586 


no 


396 


7695 


78o5 


79U 


8024 


8i34 


8243 


8353 


8462 


85 7 2 


8681 


no 


397 


8791 


8900 


9009 


9119 


9228 


9 337 
0428 


9446 


9 556 


9 665 


9774 


109 


3 9 8 


* 9883 


999 2 


♦ IOI 


0210 


o3io 


o537 


0646 


0755 


0864 


109 


3 99 


60 0973 


1082 


1191 


1299 


1408 


i5i7 


1625 


1734 


i843 


1961 


109 j 


N. 





1 


2 


3 


4 


5 


6 


1 


8 


9 


D. 



Table I. 


LOGARITHMS OF NUMBERS. 


1 


N. 





1 


2 


3 


4 


5 


6 


1 


8 


9 


D. 


4oo 


60 2060 


2169 2277 


2386 


2494 


26o3 


2711 


2819 


2928 | 3o36 


108 


4oi 


3 144 


3253 336i 


3469 


3577 


3686 


3794 


3902 


4010 | 4118 


108 


402 


4226 


4334 4442 


455o 


4658 


4766 


4874 


4982 


5089 5197 


108 


4o3 


53o5 


54i3 j 552i 1 5628 


5736 


5844 


5951 


6059 


6166 : 6274 


108 


404 


638 1 


6489 6596 


6704 


681 1 


6919 


7026 


7i33 


7241 ; 7348 


107 


4o5 


7455 


7562 i 7669 


7777 


7884 


7991 


8098 


82o5 


83 1 2 8419 


107 


406 


8326 


8633 | 8740 


8847 


8 9 54 


9061 


9167 


9274 


9 38i i 9488 


107 


407 


#9594 


9701 


9808 


9914 


♦021 


0128 


0234 


o34i 


0447 o554 


107 


408 


61 0660 


0767 


0873 


0979 


1086 


1 192 


1298 


i4o5 


i5ii 


1617 


106 


409 


1723 


1829 


1936 


2042 


2148 


2264 


236o 


2466 


2572 


2678 


106 


410 


2784 


2890 


2996 


3l02 


3207 


33i3 


3415 


3525 


363o 


3 7 36 


106 


411 


3842 


3947 4o53 


4159 


4264 


4370 


4473 


458i 


4686 i 4792 


106 


412 


4897 


5oo3 


5io8 


52i3 


53l9 


5424 


5529 


5634 


5740 5845 


io5 


4i3 


O950 


6o55 


6160 


6265 


6370 


6476 


658i 


6686 


6790 i 6895 


io5 


4i4 


7000 


7io5 


7210 


73i5 


7420 


7025 


7629 


7734 


783 9 


7943 


io5 


4i5 


8048 


8i53 


8257 


8362 


8466 


8571 


8676 


8780 


8884 


8989 


io5 


416 


* 9093 


9198 


9302 


9406 


95ll 


9615 


9719 


9824 


9928 


♦ 032 


104 


417 


62 oi36 


0240 


o344 


0448 


o552 


o656 


0760 


0864 


0968 


1072 


104 


418 


1176 


1280 


1 384 


1488 


1592 


1695 


1799 


1903 2007 


2110 


1 04 


419 


2214 


23i8 


2421 


2525 


2628 


2732 


283o 


2939 


3o42 


3i46 


104 


420 


3249 


3353 


3456 


3559 


3663 


3766 


386 9 


3973 


4076 


4179 


io3 


421 


4282 


4385 


4488 


4591 


4695 


4798 


4901 


5oo4 


5107 


5210 


io3 


422 


53i2 


54i5 


55i8 


562i 


5724 


5827 


5929 


6o32 


6i35 


6238 


io3 


423 


634o 


6443 


6546 


6648 


6751 


6853 


6956 


7o58 


7161 


7263 


io3 


424 


7366 


7468 


7571 


7673 


7775 


7878 


7980 


8082 


8i85 


8287 


102 


425 


838 9 


8491 


85 9 3 


86 9 5 


8797 


8900 


9002 


9104 


9206 


9 3o8 


102 


426 


#9410 


9512 


9613 


97i5 


9817 


9919 


♦021 


0123 


0224 


o326 


102 


427 


63 0428 


o53o 


o63i 


0733 


o835 


0936 


io38 


1139 


1241 


i342 


102 


428 


1444 


1 545 


1647 


1748 


1849 


1951 


2052 


2 1 53 


2255 


2356 


101 


429 


2457 


2559 


2660 


2761 


2862 


2963 


3 064 


3i65 


3266 


3367 


101 


43o 


3468 


356 9 


3670 


3771 


3872 


3973 


4074 


4h5 


4276 


4376 


100 


43 1 


4477 


4578 


4679 


4779 


4880 


4981 


5o8i 


5i82 


5283 


5383 


100 


432 


5484 


5584 


5685 


5 7 85 


5886 


5 9 86 


6087 


6187 


6287 


6388 


100 


433 


6488 


6588 


6688 


6789 


6889 


6989 


7089 


7189 


7290 


73go 


100 


434 


7490 


7590 


7690 


7790 


7890 


7990 


8090 


8190 


8290 


838 9 


99 


435 


8489 


858g 


8689 


8789 


8888 


8988 


9088 


9188 


9287 


9387 


99 


436 


*9486 


9586 


9686 


97 85 


9 885 


9984 


♦084 


oi83 


0283 


o382 


99 


437 


640481 


o58i 


0680 


0779 


0879 


0978 


1077 


1177 


1276 


1375 


99 


438 


1474 


i5 7 3 


1672 


1771 


1871 


•970 


2069 


2168 


2267 


2366 


99 


439 


2465 


2563 


2662 


2761 


2860 


2959 


3o58 


3i56 


3255 


3354 


99 


44o 


3453 


355i 


365o 


3749 


3847 


3946 


4o44 


4i43 


4242 


434o 


98 


44i 


4439 


4537 


4636 


4734 


4832 


4g3 1 


5029 


5127 


5226 


5324 


98 


442 


5422 


5521 


56ig 


5717 


58i5 


5913 


60 1 1 


6110 


6208 


63o6 


98 


443 


6404 


65o2 


6600 


6698 


6796 


6894 


6992 


7089 


7187 


7285 


98 


444 


7383 


748i 


7 5 79 


7676 


7774 


7872 


7969 


8067 


8i65 


8262 


98 


445 


836o 


845a 


8555 


8653 


8 7 5o 


8848 


8945 


9043 


9140 


9237 


97 


446 


* 9335 


9432 


953o 


9627 


9724 


9821 


9019 


♦016 


ou3 ; 0210 


97 


447 


65 o3o8 


o4o5 


o5o2 


0599 


0696 


0793 


0890 


0987 


1084 1181 


97 


448 


1278 


i3 7 5 


1472 


1 D69 


1666 


1762 


1859 


1956 


2o53 


2i5o 


97 


449 


2246 


2343 


2440 


2536 


2633 


2730 


2826 


2923 


3019 


3n6 


97 


45o 


32i3 


3309 
42 7 3 


34o5 I 35o2 


35 9 8 


36 9 5 


3791 


3888 


3 9 84 


4080 


96 


45 1 


4i77 


4369 4465 


4562 


4658 


4754 


485o 


4946 


5o42 


96 


432 


5i38 


5235 


533 1 


0427 


5523 


5619 


5ii5 


58io 


5906 


6002 


96 


453 


6098 


6194 


6290 


6386 


6482 


6577 


66 7 3 


6769 


6864 


6960 


96 


454 


70 56 


7162 


7247 


7343 


7438 


7534 


7629 


7725 


7820 


7916 


96 


455 


801 1 


8107 


8202 


8298 


83 9 3 


8488 


8584 


8679 


8774 


8870 


9 5 


456 


8 9 65 


9060 


9i55 


925o 


9346 


944i 


9 536 


9631 


9726 


9821 


9 5 


457 


* 9916 


♦on 


0106 


0201 


0296 


0391 


0486 


o58i 


0676 j 0771 


9 5 


458 


66 o865 


0960 


io55 


n5o 


1245 


1339 


1434 


1529 


1623 1718 


95 


459 


i8i3 


1907 


2002 


2096 


2191 


2286 


238o 


2475 


256 9 j 2663 


95 
D. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 



LOGARITHMS OF NUMBERS. 



Table I. 



460 
461 
462 
463 
464 

465 

466 
467 
468 
469 

470 

471 
472 
473 
474 

475 
476 
477 
478 
479 
480 
481 
482 
483 
484 

485 

486 
487 
488 
489 

490 
491 
492 
493 
494 

495 

496 
497 
498 

499 
5oo 
5oi 
5o2 
5o3 
5o4 

5o5 
5o6 
507 
5o8 
509 

5io 
5n 

5l2 

5i3 
5i4 

5i5 
5i6 

517 
5i8 
519 

N. 





66 2758 
3701 
4642 
558i 
65i8 

7453 
8386 

* g3i7 

67 0246 
1173 

2098 

3021 

3942 

4861 

.5778 

6694 
7607 

85i8 
#9428 

68 o336 

1 241 
2145 
3o47 
3o47 
4845 

5742 
6636 
7529 
8420 
*93c>9 

69 0196 

1081 
io65 

2847 
3727 

46o5 
5482 
6356 
7229 
8101 

8970 
* 9 838 

70 0704 
1 568 
243 1 

32QI 

4i5i 
5oo8 
5864 
6718 

7570 
8421 

* 9270 

71 0117 
0963 

1807 
265o 
3491 
433o 
5167 





2852 

3795 

4736 
5675 
6612 

7546 

8479 
9410 
o33o 
1260 

2190 
3n3 
4o34 
4q53 
5870 

6 7 85 
7698 
8609 
9 5i 9 
0426 

i332 

2235 

3i3 7 
4o37 
4g35 

583 1 
6726 
7618 
85oo 
9 3 9 8 

0285 
1170 
2o53 
2935 
38i5 

4693 
556 9 
6444 

7 3l7 

8188 

9 o5 7 
9924 
079,0 
1 654 
2617 

3377 
4236 
5094 
5949 
68o3 

7655 
85o6 
9 355 
0202 
1048 

1892 
2734 
3575 
44U 
525i 



2947 
388 9 
483o 
5769 
6705 

7640 
8572 
95o3 
o43 1 
i358 

2283 

32o5 
4126 
5o45 
5962 

6876 
7789 
8700 
9610 
o5i7 

1422 
2326 
3227 
4127 
5o25 

5921 
68i5 
7707 
85o8 
9486 

0373 
1258 
2142 
3o23 
3903 

4781 
5657 
653 1 
74o4 
8275 

9144 
♦on 
0877 
I74i 
26o3 

3463 

4322 

5i 7 q. 
6o35 



3o4i 
3983 
4924 
5862 

6799 

7733 
8665 
9596 
o524 
i45i 

2375 
3297 
4218 
5i37 
6o53 

6968 
7881 
8791 
9700 
0607 

i5i3 

2416 
33i7 
4217 
5ii4 

6010 
6904 
7796 
8687 
9 5 7 5 

0462 
1 347 

2230 

3i 1 1 

3 99 i 



7740 
85 9 i 
944o 
0287 

Il32 

1976 
2818 
365o 

4497 
5335 



5744 
6618 

749i 
8362- 

923i 
0098 
oo63 
1827 
2689. 

3549 
4408 
5265 
6120 
6974 

7826 
8676 
9524 
0371 
1217 

2060 
2902 
3742 
458i 
54i8 



3i35 
4078 
5oi8 
5 9 56 
6892 

7826 
8 7 5 9 
9689 
0617 
1 543 

2467 
3390 
43io 
5228 
6i45 

7059 
7972 
8882 
9791 
0698 

i6o3 
25o6 
3407 
4307 
5204 

6100 
6994 

7886 
8776 
9664 

o55o 
1435 
23i8 

3i99 
4078 

4956 
5832 
6706 
^578 
8449 

9 3i 7 
0184 
io5o 
1913 

2775 

3635 
4494 
535o 
6206 
7o5 9 

79.11 
8761 
9609 
0456 
i3oi 

2144 
2986 
3826 
4665 
55o2 



323o 
4172 

5lI2 

6o5o 
6986 

7920 
8852 
9782 
0710 
1 636 

256o 
3482 
4402 
5320 
6236 

7i5i 
8o63 
8973 
9882 
0789 

i6g3 
2596 

3497 
4396 

5294 

6189 
7o83 

w 5 

8865 
9753. 

0639 
i524 
2406 
3287 
4166 

5o44 
5 9 i 9 
6793 
7665 
8535 

9404 
0271 
u36 

1999 
2861 

3721 
4579 
5436 
6291 
7144 

7996 
8846 
969,4 
o54o 
i385 

2229 
3070 
3910 

4749 
5586 



6 



3324 
4266 
52o6 
6i43 
7079 

8oi3 
8945 
9875 
0802 
1728 

2652 

3574 
4494 

5412 
6328 

7242 
8i54 
9064 

9973 
0879 

1784 
2686 
3587 
4486 
5383 

6279 
7172 
8064 
8o53 
9841 

0728 
1612 
2494 
3375 
4254 

5i3i 

6007 



7752 
8622 

9491 
o358 
1222 
2086 
2947 

3807 
4665 

5522 

6376 

7229 

8081 
8931 

9779 
062D 

1470 

23i3 
3i54 
3994 
4833 
566 9 



34i8 
436o 
5299 
62J7 
7173 

8106 
9038 
9967 
0895 
1821 

2744 
3666 
4586 
55o3 
6419 

7 333 
8245 
9i55 
♦o63 
0970 

1874 

2777 
3677 
4576 
5473 

6368 
7261 
8i53 
9042 
9930 

0816 
1700 
2583 
3463 
4342 

5219 
6094 
6968 

r 3 9 
8709 

9 5 7 8 
0444 
1 309 
2172 

3o33 

38o5 
4751 
5607 
6462 
73i5 

8166 
9015 

9863 
0710 
i554 

2397 
3238 
4078 
4916 
5 7 53 



35i2 
4454 
53 9 3 
633 1 
7266 

8199 
9i3i 
♦060 
0988 
1913 

2836 
3 7 58 
4677 
55 9 5 
65u 

7424 
8336 
9246 
oi54 
1060 

1964 
2867 

3767 
4666 
5563 

6458 
7 35i 
8242 
9i3i 
♦019 

0905 
1789 
2671 
355i 
443o 

53o7 
6182 
7055 
7926 
8796 

9664 
o53i 
i3 9 5 

2258 

3119 

3979 
4837 

56 9 3 
6547 
74oo 

825i 
9100 
9948 
0794 
1639 

2481 
3323 
4162 
5ooo 
5836 



3607 
4548 
5487 
6424 
736o 

8293 
9224 
oi53 
1080 
2oo5 

2929 
385o 

4769 
568 7 
6602 

75i6 
8427 
9337 
0245 
n5i 

2o55 
2957 
3857 
4756 
5652 

6547 
744o 
833i 
9220 
0107 

0993 
1877 
2759 
363 9 
45i7 

53 9 4 
6269 
7U2 
8014 

8883 

975i 
0617 
1482 
2,344 
32o5 

4o65 
4922 
5 77 8 
6632 
7485 

8336 
9i85 
♦o33 
0879 
172J 

2566 
3407 
4246 
5o84 
5920 



D. 

94 
9 4 
9 4 
94 
94 

93 
93 
93 

93 

93 

92 
92 
92 

92 
02 

91 
91 
9 1 
91 
9i 
90 
90 
90 
90 
90 

29 

?9 
?9 
^9 
89 



87 

*? 
87 

8 J 
87 
86 
86 
86 

86 

86 
86 
85 
85 

85 

85 
85 
85 
84 

84 
84 
84 
84 
84 

D. 



Table I. 


LOGARITHMS OF NUMBERS. 


9 


520 





1 
1 2 


3 


4 


5 


6 


7 


8 


9 


D. 


71 6oo3 


6087 


6170 


6254 


6337 


6421 


65o4 


6588 


6671 


6754 


83 


521 


6838 


6921 


7004 


7088 


7171 


7254 


7338 


742i 


75o4 


7 58 7 


83 


522 


7671 


7754 


7837 


7920 


8oo3 


8086 


8169 


8253 


8336 


8419 


83 


523 


85o2 


8585 


8668 


8 7 5i 


8834 


8917 


9000 


9083 


9165 


9248 


83 


524 


* 933i 


9414 


9497 


9080 


9 663 


9745 


9828 


991 1 


9994 


♦077 


83 


525 


72 0159 


0242 


o325 


0407 


0490 


0573 


o655 


0738 


0821 


0903 


83 


526 


0986 


1068 


ii5i 


1233 


i3i6 


i3 9 8 


1481 


1 563 


1646 


1728 


82 


527 


1811 


i8 9 3 


1975 


2o58 


2140 


2222 


23o5 


2387 


2469 


2552 


82 


528 


2634 


2716 


2798 


2881 


2963 


3o45 


3127 


3209 


3291 


3374 


82 


529 


3456 


3538 


3620 


3702 


3784 


3866 


3 9 48 


4o3o 


4112 


4194 


82 


53o 


4276 


4358 


444o 


4522 


4604 


4685 


4767 


4849 


493i 


5oi3 


82 


53 1 


5095 


6176 


5258 


5340 


5422 


55o3 


5585 


566 7 


5 7 48 


583o 


82 


532 


5912 


5 99 3 


6075 


6i56 


6238 


6320 


6401 


6483 


6564 


6646 


82 


533 


6727 


6809 


6890 


6972 


7o53 


7i34 


7216 


7297 


7379 


7460 


81 


534 


754i 


7623 


7704 


77 85 


7866 


7948 


8029 


8110 


8191 


8273 


81 


535 


8354 


8435 


85i6 


85 9 7 
9408 


8678 


8 7 5 9 


8841 


8922 


9003 


9084 


81 


536 


9i65 


9246 


9 32 7 


948o 


9 5 7 o 


965i 


9732 


9813 


9 8 9 3 


81 


537 


* 997 4 


♦o55 


oi36 


0217 


0298 


o3 7 8 


0459 


o54o 


0621 


0702 


81 


538 


73 0782 


o863 


0944 


1024 


no5 


1 186 


1266 


1 347 


U28 


i5o8 


81 


53 9 


i58 9 


1669 


1750 


i83o 


1911 


1991 


2072 


2l52 


2233 


23i3 


81 


54o 


2394 


2474 


2555 


2635 


2715 


2796 


2876 


2956 


3o37 


3117 


80 


54i 


3i 97 


3^78 


3358 


3438 


35i8 


35 9 8 


3679 


3759 


383 9 


3 9 i 9 


80 


542 


3999 


4079 


4160 


4240 


4320 


44oo 


4480 


456o 


4640 


4720 


80 


543 


4800 


4880 


4960 


5o4o 


5l20 


5200 


5279 


535 9 


5439 


55i9 


80 


544 


5599 


56 79 


5 7 5 9 


5838 


5 9 i8 


5998 


6078 


6157 


6237 


63i 7 


80 


545 


63 97 


6476 


6556 


6635 


6 7 i5 


6795 


6874 


6954 


7o34 


71 13 


80 


546 


7io3 


7272 


7 352 


743 1 


761 1 


7590 


7670 


7749 


7829 


7908 


79 


547 


7987 


8067 


8146 


8225 


83o5 


8384 


8463 


8543 


8622 


8701 


79 


548 


8781 


8860 


8 9 3 9 


9018 


9097 


9177 


9256 


9 335 


9414 


94q3 


79 


549 


45-9572 


965i 


9731 


9810 


9889 


9968 


♦047 


0126 


0205 


0284 


79 


55o 


74 o363 


0442 


0521 


0600 


0678 


0757 


o836 


0915 


0994 


1073 


79 


55i 


Il52 


I23o 


1309 


i388 


1467 


1 546 


1624 


1703 


1782 


i860 


79 


552 


i 9 3o 
2725 


2018 


2096 


2175 


2254 


2332 


241 1 


2489 


2568 


2646 


79 


553 


2804 


2882 


2961 


3o39 


3n8 


3196 


3275 


3353 


343 1 


78 


554 


35io 


3588 


3667 


3745 


3823 


3902 


3 9 8o 


4o58 


4i36 


42i5 


78 


555 


4293 


4371 


4449 


4528 


4606 


4684 


4762 


4840 


4919 


4997 


78 


556 


5075 


5i53 


523i 


5309 


538 7 


5465 


5543 


562i 


5699 


5777 


78 


557 


5855 


5 9 33 


601 1 


6089 


6167 


6245 


6323 


6401 


6479 


6556 


78 


558 


6634 


6712 


6790 


6868 


6945 


7023 


7101 


7179 


7256 


7334 


78 


55 9 


7412 


7489 


7567 


7645 


7722 


7800 


7878 


79 55 


8o33 


8110 


78 


56o 


8188 


8266 


8343 


8421 


8498 


8576 


8653 


8731 


8808 


8885 


77 


56i 


8 9 63 


9040 


9118 


9 i 9 5 


9272 


935o 


9427 


95o4 


9582 


9659 


77 


562 


#9736 


9814 


9891 


9968 


♦o45 


0123 


0200 


0277 


o354 


o43 1 


77 


563 


75 o5o8 


o586 


o663 


0740 


0817 


0894 


0971 


1048 


1 125 


1202 


77 


564 


1279 


i356 


1433 


i5io 


1 58 7 


1664 


1741 


1818 


i8 9 5 


1972 


77 


565 


2048 


2125 


2202 


2279 


2356 


2433 


2 509 


2586 


2663 


2740 


77 


566 


2816 


2893 


2970 


3o47 


3i23 


3200 


3277 


3353 


343o 


35o6 


77 


567 


3583 


366o 


3 7 36 


38i3 


388 9 


3966 


4042 


4119 


4195 


4272 


77 


568 


4348 


4425 


45oi 


4578 


4654 


4730 


4807 


4883 


4960 


5o36 


76 


56 9 


5lI2 


5i8 9 


5265 


534i 


5417 


5494 


5570 


5646 


5722 


5799 


76 


570 


5875 


5951 


6027 


6io3 


6180 


6256 


6332 


6408 


6484 


656o 


76 


571 


6636 


6712 


6788 


6864 6940 


7016 


7092 


7168 


7244 


7320 


76 


572 


7396 


7472 


7548 


7624 


7700 


7775 


785i 


7927 


8oo3 


8079 


76 


5 7 3 


8i55 


823o 


83o6 


8382 


8458 


8533 


8609 


8685 


8761 


8836 


76 


574 


8912 


8988 


9063 


9 i3 9 


92U 


9290 


9 366 


9441 


9517 


9592 


76 


5 7 5 


# 9668 


9743 


9819 


9894 


9970 


♦045 


0121 


0196 


0272 


o347 


75 


576 


76 0422 


0498 


0573 


0649 


0724 


0799 


0875 


0960 


1025 


IIOI 


75 


577 


1176 


1201 


i326 


1402 


1477 


i552 


1627 


1702 


1778 


i853 


75 


5 7 8 


1928 


2003 


2078 


2i53 


2228 


23o3 


2378 


2453 


252Q 


2604 


75 


5 79 


2679 


2754 


2829 


2904 


2978 


3o53 


3x28 


32o3 


3278 


3353 


75 , 


N. 





1 


2 


8 


4 


5 


6 


7 


8 


9 


P. 



10 




LOGARITHMS OF NUMBERS. Table I 


N. 





1 


2 


3 


4 


5 


6 


1 


8 


9 


D. 


58o 


763428 


35o3 


35 7 8 


3653 


3727 


38o2 


38 77 


3g52 


4027 


4101 


75 


58i 


4176 


425i 


4326 


4400 


4475 


455o 


4624 


4699 


4774 


4848 


7 5 


582 


4923 


499 8 


5072 


5i47 


5221 


5296 


5370 


5445 


5520 


5594 


75 


583 


566 9 


5 7 43 


58i8 


58 9 2 


5 9 66 


6041 


6u5 


6190 


6264 


6338 


74 


584 


64i3 


6487 


6562 


6636 


6710 


6 7 85 


685 9 


6 9 33 


7007 


7082 


74 


585 


7 i56 


723o 


73o4 


7379 


7453 


7527 


7601 


7675 


7749 


7823 


74 


586 


7898 


7972 


8046 


8120 


8194 


8268 


8342 


8416 


8490 


8564 


74 


58 7 


8638 


8712 


8786 


8860 


8 9 34 


9008 


9082 


9i56 


9230 


93o3 


74 


588 


*9 3 77 


945 1 


9525 


9 5 99 


9673 


9746 


9820 


9894 


9968 


♦042 


74 


58 9 


77 oii5 


0189 


0263 


o336 


0410 


0484 


o557 


o63i 


0705 


0778 


74 


590 


o852 


0926 


0999 


1073 


1 146 


1220 


1293 


i36 7 


1440 


i5i4 


74 


591 


i58 7 


1661 


1734 


1808 


1881 


1955 


2028 


2102 


2175 


2248 


73 


592 


2322 


2395 


2468 


2542 


26i5 


2688 


2762 


2835 


2908 


2981 


73 


593 


3o55 


3i28 


3201 


3274 


3348 


3421 


3494 


356 7 


364o 


37i3 


73 


594 


3786 


386o 


3 9 33 


4006 


4079 


4i52 


4225 


4298 


4371 


4444 


73 


595 


45i7 


4590 


4663 


4736 


4809 


4882 


4955 


5o28 


5ioo 


5i73 


73 


5 9 6 


5246 


5319 


5392 


5465 


5538 


56io 


5683 


5 7 56 


5829 


5902 


73 


597 


5974 


6047 


6120 


6193 


6265 


6338 


641 1 


6483 


6556 


6629 


73 


5 9 8 


6701 


6774 


6846 


6919 


6992 


7064 


7137 


7209 


7282 


7354 


73 


5 99 


7427 


7499 


7 5 7 2 


7644 


7717 


7789 


7862 


79 3 4 


8006 


8079 


72 


600 


8i5i 


8224 


8296 


8368 


844i 


85i3 


8585 


8658 


8730 


8802 


72 


601 


8874 


8947 


9019 


9°9* 


9163 


9236 


93o8 


9 38o 


9452 


9524 


72 


602 


•55-9596 


9669 


974i 


9 8i3 


9 885 


99 5 7 


♦029 


0101 


0173 


0245 


72 


6o3 


780317 


o38 9 


0461 


o533 


o6o5 


0677 


0749 


0821 


o8 9 3 


0965 


72 


604 


1037 


1 1 09 


1181 


1253 


i324 


1396 


1468 


1 54o 


1612 


1684 


72 


6o5 


i 7 55 


1827 


1899 


1971 


2042 


2H4 


2186 


2258 


2329 


2401 


72 


606 


2473 


2544 


2616 


2688 


2759 


283 1 


2902 


2974 


3o46 


3117 


72 


607 


3i8 9 


326o 


3332 


34o3 


3475 


3546 


36i8 


368 9 


3761 


3832 


7i 


608 


3904 


3975 


4046 


4118 


4189 


4261 


4332 


44o3 


4475 


4546 


7i 


609 


4617 


4689 


4760 


483 1 


4902 


4974 


5o45 


5u6 


5i8 7 


5259 


7i 


610 


533o 


54oi 


5472 


5543 


56i5 


5686 


5757 


5828 


58 99 


5970 


7i 


611 


6o4i 


6112 


6i83 


6254 


6325 


63 9 6 


6467 


6538 


6609 


6680 


7i 


612 


6 7 5i 


6822 


68 9 3 


6964 


7o35 


7106 


7177 


7248 


73i 9 


73 9 o 


7i 


6i3 


7460 


753i 


7602 


7673 


7744 


7815 


7885 


79 56 


8027 


8098 


71 


614 


8168 


823 9 


83io 


838i 


845 1 


8522 


85 9 3 


8663 


8 7 34 


8804 


7i 


6i5 


8875 


8946 


9016 


9087 


9157 


9228 


9299 


9369 


944o 


95io 


71 


616 


*958i 


965 1 


9722 


9792 


9 863 


9933 


♦004 


0074 


0144 


02 1 5 


70 


617 


79 0285 


o356 


0426 


0496 


0567 


0637 


0707 


0778 


0848 


0918 


70 


618 


0988 


1059 


1129 


1 199 


1269 


i34o 


1410 


1480 


i55o 


1620 


70 


619 


1691 


1761 


i83i 


1901 


1971 


2041 


2111 


2181 


2252 


2322 


70 


620 


2392 


2462 


2532 


2602 


2672 


2742 


2812 


2882 


2952 


3022 


70 


621 


3092 


3i62 


323i 


33oi 


33 7 i 


344i 


35n 


358i 


365i 


3721 


70 


622 


3790 


386o 


3930 


4000 


4070 


4139 


4209 


4279 


434Q 


44l8 


70 


623 


4488 


4558 


4627 


4697 


4767 


4836 


4906 


4976 


5o45 


5u5 


70 


624 


5i85. 


5254 


5324 


53 9 3 


5463 


5532 


56o2 


5672 


574i 


58u 


70 


625 


588o 


5949 


6019 


6088 


6i58 


6227 


6297 


6366 


6436 


65o5 


69 


626 


65 7 4 


6644 


6 7 i3 


6782 


6852 


6921 


6990 


7060 


7129 


7198 


69 


627 


7268 


7337 


74o6 


7475 


7545 


7614 


7683 


7752 


7821 


7890 


69 


'628 


7960 


8029 


8098 


8167 


8236 


83o5 


83 7 4 


8443 


85i3 


8582 


69 


629 


865i 


8720 


8789 


8858 


8927 


8996 


9065 


9134 


9203 


9272 


69 


63o 


934i 


9409 


9478 


9 547 


9616 


9 685 


97 5 4 


9823 


9892 


9961 


i 9 


63 1 


80 0029 


0098 


0167 


0236 


o3o5 


0373 


0442 


o5u 


o58o 


0648 


69 


632 


0717 


0786 


o854 


0923 


0992 


1061 


1 1 29 


1198 


1266 


i335 


69 


633 


1404 


1472 


i54i 


1609 


1678 


1747 


i8i5 


1884 


1952 


2021 


69 


634 


2089 


2i58 


2226 


2295 


2363 


2432 


25oo 


2568 


2637 


2705 


69. 


635 


2774 


2842 


2910 


2979 


3o47 


3n6 


3i84 


3252 


332i 


338 9 


68 


636 


3457 


3525 


35 9 4 


3662 


3730 


3798 


3867 


3935 


4oo3 


4071 


68 


637 


4139 


4208 


4276 


4344 


4412 


4480 


4548 


4616 


4685 


4753 


68 


638 


4821 


4889 


4957 


5o25 


5093 


5i6i 


522Q 


5297 


5365 


5433 


68 


63 9 


55oi 


556 9 


5637 



I - 


5705 


5773 


584i 


5908 


5976 


6044 


6112 


68 
D. 


K. 





1 


3 


4 


5 


6 


7 


8 


9 



Table I. 


LOGARITHMS OF NUMBERS. 


11 


N. 





1 


2 


3 


4 


5 


6 


1 


8 


9 


D. 


640 


806180 


6248 


63i6 


6384 


645i 


65i9 


658 7 


6655 


6723 


6790 


68 


641 


6858 


6926 ! 6994 


7061 


7129 


7197 


7264 


7332 


7400 


7467 


68 


642 


7535 


7603 


7670 


77 38 


7806 


7873 


794i 


8008 


8076 


8i43 


68 


643 


8211 


8279 


8346 


84i4 


8481 


8549 


8616 


8684 


8751 


8818 


67 


644 


8886 


8 9 53 


9021 


9088 


9i56 


9223 


9290 


9 358 


9425 


9492 


67 


645 


-x 9560 


9627 


9694 


9762 


9829 


9896 


9964 


♦o3i 


0098 


oi65 


6 7 


646 
647 


8i0233 


o3oo 


0367 


0434 


o5oi 


0569 


o636 


0703 


0770 


0837 


67 


0904 


0971 


1039 


1106 


1 173 


1240 


1307 


i374 


i44i 


i5o8 


67 


648 


i575 


1642 


1709 


1776 


i843 


1910 


1977 


2044 


2111 


2178 


67 


649 


2245 


23l2 


2379 


2445 


25l2 


2579 


2646 


2713 


2780 


2847 


67 


65o 


2913 


2980 


3 047 


3n4 


3i8i 


3247 


33i4 


338i 


3448 


35i4 


67 


65i 


358i 


3648 


3714 


3 7 8i 


3848 


3914 


3 9 8i 


4048 


4n4 


41 81 


67 


652 
653 


4248 


43 14 


438 1 


4447 


45i4 


458 1 


4647 


47U 


4780 


4847 


67 


49i3 


4980 


5o46 


5n3 


6179 


5246 


53 1 2 


5378 


5445 


55u 


66 


654 


5578 


5644 


57 1 1 


5777 


5843 


5910 


5 97 6 


6042 


6109 


6175 


66 
66 


655 


6241 


63o8 


63 7 4 


6440 


65o6 


65 7 3 


663 9 


6705 


6771 


6838 


656 


6904 


6970 


7o36 


7102 


7169 


7235 


73oi 


7 36 7 


7433 


7499 


66 


657 


7565 


763 1 


7698 


7764 


783o 


7896 


7962 


8028 


8094 


8160 


66 


658 


8226 


8292 


8358 


8424 


8490 


8556 


8622 


8688 


8754 


8820 


66 


65 9 


8885 


8 9 5i 


9017 


9 o83 


9149 


9215 


9281 


9346 


94i2 


9478 


66 


660 


*9544 


9610 


9676 


974i 


9807 


9873 


99 3 9 


♦004 


0070 


oi36 


66 


661 


82 0201 


0267 


o333 


0399 


0464 


o53o 


0595 


0661 


0727 


0792 


66 


662 


o858 


0924 


0989 


io55 


1120 


1 186 


I25l 


1317 


i382 


1448 


66 


663 


i5i4 


1 5 79 


i645 


1710 


1775 


1 841 


1906 


1972 


2037 


2103 


65 


664 


2168 


2233 


2299 


2364 


243o 


2495 


256o 


2626 


2691 


2756 


65 


665 


2822 


2887 


2952 


3oi8 


3o83 


3 148 


32i3 


3279 


3344 


3409 


65 


666 


3474 


3539 


36o5 


3670 


3 7 35 


38oo 


3865 


3930 


3996 


4061 


65 


667 


4126 


4191 


4256 


432i 


4386 


445 1 


45i6 


458i 


4646 


47 1 1 


65 


668 


4776 


4841 


4906 


4971 


5o36 


5ioi 


5i66 


523i 


5296 


536i 


65 


669 


5426 


5491 


5556 


5621 


5686 


575i 


58i5 


588o 


5945 


6010 


65 


670 


6075 


6140 


6204 


6269 


6334 


6399 


6464 


6528 


65g3 


6658 


65 


671 


6723 


6787 


6852 


6917 


6981 


7046 


71 1 1 


7175 


7240 


73o5 


65 


672 


7369 


7434 


7499 


7563 


7628 


7692 


7757 


7821 


7886 


795i 


65 


6 7 3 


8oi5 


8080 


8i44 


8209 


82 7 3 


8338 


8402 


8467 


853i 


8395 


64 


674 


8660 


8724 


8789 


8853 


8918 


8982 


9046 


9111 


9175 


9239 


64 


6 7 5 


9304 


9 368 


9432 


9497 


956i 


9625 


9690 


9754 


9818 


9882 


64 


676 


* 9947 


♦on 


0075 


0139 


0204 


0268 


o332 


0396 


0460 


o525 


64 


677 


83 o58 9 


o653 


0717 


0781 


0845 


0909 


0973 


1037 


1102 


1 166 


64 


678 


I23o 


1294 


i358 


1422 


i486 


IDDO 


1614 


1678 


1742 


1806 


64 


679 


1870 


1934 


1998 


2062 


2126 


2189 


2253 


2317 


238i 


2445 


64 


j 680 


2509 


2573 


2637 


2700 


2764 


2828 


2892 


2956 


3020 


3o83 


64 


| 681 


3i47 


3211 


3275 


3338 


3402 


3466 


353o 


35 9 3 


3657 


3721 


64 


1 682 


3 7 84 


3848 


3912 


3975 


4039 


4io3 


4166 


423o 


4294 


4357 


64 


683 


442i 


4484 


4548 


4611 


4675 


4739 


4802 


4866 


4929 


4993 


64 


684 


5o56 


5l20 


5i83 


5247 


53io 


5373 


543 7 


55oo 


5564 


5627 


63 


685 


5691 


5754 


58i 7 


588i 


5944 


6007 


6071 


6i34 


6197 


6261 


63 


686 


6324 


638 7 


645i 


65i4 


6577 


6641 


6704 


6767 


683o 


6894 


63 


687 


6 ?o2 


7020 


7083 


7146 


7210 


7273 


7336 


7399 


7462 


7525 


63 


688 


7588 


7652 


77i5 


7778 


7841 


7904 


7967 


8o3o 


8o 9 3 


8i56 


63 


689 
690 


8219 


8282 


8345 


8408 


8471 


8534 


85 97 


8660 


8723 


8786 


63 


8849 


8912 


8 97 5 


9 o38 


9101 


9164 


9227 


9289 


9352 


941 5 


63 


691 


* 9478 


9541 


9604 


9667 


9729 


9792 


9 855 


9918 


9981 


♦043 


63 


692 


84 0106 


0169 


0232 


0294 


o357 


0420 


0482 


o545 


0608 


0671 


63 


6 9 3 


0733 


0796 


o85 9 


0921 


0984 


1046 


1 1 09 


1 172 


1234 


1297 


63 


694 


1359 


1422 


1485 


1547 


1610 


1672 


1735 


H97 


i860 


1922 


63 


6 9 5 


i 9 85 


2047 


2110 


2172 


2235 


2297 


236o 


2422 


2484 


2547 


62 


696 


2609 


2672 


2734 


2796 


285 9 


2921 


2 9 83 


3 046 


3io8 


3170 


62 


697 


3233 


3295 


3357 


3420 


3482 


3544 


36o6 


366 9 


373i 


3793 


62 


698 


3855 


3 9 i8 


3 9 8o 


4042 


4104 


4166 


4229 


4291 


4353 


44i5 


62 


699 


4477 


453 9 


4601 
2 


4664 


4726 


4788 


485o 


4912 


4974 


5o36 


62 


K 





1 


3 


4 


5 


6 


1 


8 


9 


D. 



12 




LOGARITHMS OF NUMBERS. Table I. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


D. 


700 


84 5o 9 8 


5i6o 


5222 


5284 


5346 


5408 


5470 


5532 


5594 


5656 


62 


701 


5 7 i8 


5780 


5842 


5904 


5 9 66 


6028 


6090 


6i5i 


62i3 


6275 


62 


702 


6337 


6399 


6461 


6523 


6585 


6646 


6708 


6770 


6832 


6894 


62 


7o3 


6o55 


7017 


7079 


7141 


7202 


7264 


7326 


7388 


7449 


75u 


62 


704 


7573 


7634 


7696 


77 58 


7819 


7881 


7943 


8004 


8066 


8128 


62 


705 


8189 


825i 


83i2 


83 7 4 


8435 


8497 


855 9 


8620 


8682 


8743 


62 


706 


88o5 


8866 


8928 


8989 


9o5i 


9112 


9174 


9235 


9297 


9 358 


61 


707 


9419 


9481 


9542 


9604 


9 665 


9726 


9788 


9849 


991 1 


9972 


61 


708 


85 oo33 


0095 


01 56 


0217 


0279 


o34o 


0401 


0462 


o524 


o585 


61 


709 


0646 


0707 


0769 


o83o 


0891 


0952 


1014 


1075 


n36 


1197 


61 


710 


1258 


l320 


i38i 


1442 


i5o3 


1 564 


1625 


1686 


1747 
2358 


1809 


61 


711 


1870 


i^3i 


1992 


2o53 


2114 


2175 


2236 


2297 


2419 


61 


712 


2480 


2341 


2602 


2663 


2724 


2785 


2846 


2907 


2968 


3029 


61 


7 i3 


3090 


3i5o 


3211 


3272 


3333 


33 9 4 


3455 


35i6 


35 77 


3637 


61 


7U 


36 9 8 


3759 


3820 


388i 


3941 


4002 


4o63 


4124 


4i85 


4245 


61 


7 i5 


43o6 


436 7 


4428 


4488 


4549 


4610 


4670 


473i 


4792 


4852 


61 


716 


49i3 


4974 


5o34 


5095 


5i56 


52i6 


5277 


5337 


53 9 8 


5459 


61 


7i7 


5519 


558o 


564o 


5701 


5761 


5822 


5882 


5 9 43 


6oo3 


6064 


61 


718 


6124 


6i85 


6245 


63o6 


6366 


6427 


6487 


6548 


6608 


6668 


60 


719 


6729 


6789 


685o 


6910 


6970 


7o3i 


7091 


7i52 


7212 


7272 


60 


720 


7332 


7 3 9 3 


7453 


75i3 


7574 


7634 


7694 


77 55 


78i5 


7875 


60 


721 


7935 


799 5 


8o56 


8116 


8176 


8236 


8297 


8357 


8417 


8477 


60 


722 


853 7 


85 9 7 


8657 


8718 


8778 


8838 


8898 


8 9 58 


9018 


9078 


60 


723 


9 i38 


9198 


9258 


9 3i8 


9 3 79 


9439 


9499 


9S59 


9619 


9679 


60 


724 


*97 3 9 


9799 


9 85 9 


9918 


9978 


♦o38 


0098 


oi58 


0218 


0278 


60 


725 


86 o338 


0398 


0458 


o5i8 


0578 


0637 


0697 


0757 


0817 


0877 


60 


726 


0937 


0996 


io56 


1 1 16 


1 176 


1236 


1295 


i355 


I4i5 


1475 


60 


727 


1 534 


1594 


1 654 


1714 


1773 


i833 


i8 9 3 


1952 


2012 


2072 


60 


728 


2l3l 


2191 


225l 


23lO 


2370 


243o 


2489 
3o85 


2549 


2608 


2668 


60 


729 


2728 


2787 


2847 


2906 


2966 


3o25 


3i44 


3204 


3263 


60 


73o 


3323 


3382 


3442 


35oi 


356i 


3620 


368o 


3739 


3799 


3858 


5 9 


7 3i 


3oi 7 


3977 


4o36 


4096 


4i55 


4214 


4274 


4333 


4392 


4452 


59 


732 


45n 


4570 


463o 


4689 


4748 


4808 


4867 


4926 


4985 


5o45 


5o 


733 


5io4 


5i63 


5222 


5282 


534i 


54oo 


5459 


5619 


5578 


5637 


5 9 


734 


56 9 6 


5 7 55 


58i4 


58 7 4 


5 9 33 


5992 


6o5i 


6110 


6169 


6228 


59 


735 


6287 


6346 


64o5 


6465 


6524 


6583 


6642 


6701 


6760 


6819 


5 9 


736 


6878 


6937 


6996 


7o55 


7114 


7173 


7232 


7291 


735o 


7409 


59 


737 


7467 


7526 


7585 


7644 


7703 


7762 


7821 


7880 


79 3 9 


7998 


5 9 


738 


8o56 


8u5 


8174 


8233 


8292 


835o 


8409 


8468 


8527 


8586 


5? 


739 


8644 


8703 


8762 


8821 


8879 


8 9 38 


8997 


9056 


9114 


9173 


59 


74o 


9232 


9290 


934Q 


9408 


9466 


9525 


9D84 


9642 


9701 


9760 


5 9 


74i 


*98i8 


9877 


9 9 35 


9994 


♦o53 


0111 


0170 


0228 


0287 


o345 


5 9 


742 


87 0404 


0462 


0521 


0579 


o638 


0696 


0755 


o8i3 


0872 


0930 


58 


743 


0980 


1047 


1 1 06 


1 164 


1223 


1281 


i339 


i3o8 


1 456 


i5i5 


58 


744 


1573 


i63i 


1690 


1748 


1806 


1 865 


1923 


1981 


2040 


2098 


58 


745 


2 1 56 


22l5 


2273 


233i 


238 9 


2448 


25o6 


2564 


2622 


2681 


58 


746 


2739 


2797 


2855 


2913 


2972 


3o3o 


3o88 


3i46 


3204 


3262 


58 


747 


332i 


3379 


3437 


3495 


3553 


36n 


366 9 


3727 


3785 


3844 


58 


748 


3902 


3960 


4018 


4076 


4i34 


4192 


425o 


43o8 


4366 


4424 


58 


749 


4482 


4540 


45 9 8 


4656 


47i4 


4772 


483o 


4888 


4945 


5oo3 


58 


75o 


5o6i 


5no 


5i 77 


5235 


5293 


535i 


5409 


5466 


5524 


5582 


58 


7 5i 


564o 


56 9 8 


5 7 56 


58i3 


58 7 i 


5929 


5987 


6045 


6102 


6160 


58 


7 52 


6218 


6276 


6333 


6391 


6449 


6607 


6564 


6622 


6680 


6737 


58 


753 


6795 


6853 


6910 


6968 


7026 


7083 


7U1 


7199 


7256 


73i4 


58 


754 


7371 


7429 


7487 


7544 


7602 


7659 


7717 


7774 


7832 


7889 


58 


7 55 


7947 


8004 


8062 


8119 


8177 


8234 


8292 


8349 


8407 


8464 


57 


756 


8522 


85 79 


8637 


8694 


8752 


8809 


8866 


8924 


8981 


9039 


57 


7 5 7 


9096 


9i53 


9211 


9268 


9325 


9 383 


9440 


9497 


9 555 


9612 


57 


758 


#9669 


9726 


9784 


9841 


9898 


9956 


♦oi3 


0070 


0127 


oi85 


57 


7 5 9 


880242 


0299 


o356 
2 


041 3 
3 


0471 


o528 


o585 


0642 


0699 


0756 


57 


N. 





1 


4 


5 


6 


1 


8 


9 


D 



Table I. 


LOGARITHMS OF NUMBERS. 


13 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


D. 


760 


880814 


0871 


0928 


0985 


1042 


1099 


n56 


I2l3 


1271 


i328 


57 


761 


i385 


1442 


1499 


1 556 


i6i3 


1670 


1727 


1784 


1841 


1898 


5 7 


762 


io55 


2012 


2069 


2126 


2i83 


2240 


2297 


2354 


241 1 


2468 


07 


763 


2025 


258i 


2638 


2695 


2752 


2809 


2866 


2923 


2980 


3o37 


57 


764 


3093 


3i5o 


3207 


3264 


332i 


33 77 


3434 


3491 


3548 


36o5 


5 7 i 


7 65 


366 1 


3718 


3 77 5 


3832 


3888 


3o45 


4002 


4039 


4u5 


4172 


5 7 


766 


4229 
4793 


4285 


4342 


4399 


4455 


4612 


4569 


4625 


4682 


4739 


57 


767 


4852 


4909 


4965 


5022 


5078 


5i35 


5192 


5248 


53o5 


5 7 


768 


536i 


5418 


5474 


553i 


558 7 


5644 


5700 


5707 


58i3 


5870 


5 7 


769 


5926 


5 9 83 


6039 


6096 


6i52 


6209 


6265 


632i 


6378 


6434 


56 


770 


6491 


6547 


6604 


6660 


6716 


6773 


6829 


6885 


6942 


6998 


56 


771 


7004 


7111 


7167 


7223 


7280 


7336 


7 3 9 2 


7449 


75o5 


756i 


56 


772 


7617 


7674 


773o 


7786 


7842 


7898 


7 9 55 


801 1 


8067 


8i23 


56 


773 


8179 


8236 


8292 


8348 


8404 


8460 


85i6 


8573 


8629 


8685 


56 


774 


8741 


8797 


8853 


8909 


8 9 65 


9021 


9077 


9134 


9190 


9246 


56 


77 5 


9302 


9 358 


94U 


9470 


9526 


9582 


9 638 


9694 


975o 


9806 


56 


776 


#9862 


9918 


9974 


♦o3o 


0086 


0141 


0197 


0253 


0309 


o365 


56 


777 


890421 


0477 


o533 


0589 


0645 


0700 


0706 


0812 


0868 


0924 


56 


778 


0980 


io35 


1091 


1 147 


1203 


1259 


i3i4 


1370 


1426 


1482 


56 


779 


i537 


i593 


1649 


1705 


1760 


1816 


1872 


1928 


1983 


2039 


56 


780 


2095 


2i5o 


2206 


2262 


2317 


2373 


2429 


2484 


254o 


2595 


56 


781 


265i 


2707 


2762 


2818 


2873 


2929 


2 9 85 


3o4o 


3096 


3i5i 


56 


782 


3207 


3262 


33i8 


3373 


3429 


3484 


354o 


35 9 5 


365i 


3706 


56 


7 83 


3762 


3817 


38 7 3 


3 9 28 


3 9 84 


4039 


4094 


41 5o 


42o5 


4261 


55 


784 


43i6 


4371 


4427 


4482 


4538 


4593 


4648 


4704 


4759 


4814 


55 


785 


4870 


4o25 


4980 


5o36 


5091 


5i46 


5201 


5257 


53i2 


5367 


55 


786 


5423 


5478 


5533 


5588 


5644 


5699 


5754 


58o 9 


5864 


5920 


55 


787 


5975 


6o3o 


6o85 


6140 


6195 


6261 


63o6 


636i 


6416 


6471 


55 


788 


6526 


658i 


6636 


6692 


6747 


6802 


685 7 


6912 


6967 


7022 


55 


789 


7077 


7i32 


7187 


7242 


7297 


7352 


7407 


7462 


7 5i 7 


7572 


55 j 


790 


7627 


7682 


7737 


7792 


7847 


7902 


7957 


8012 


8067 


8122 


55 


791 


8176 


823i 


8286 


834i 


83 9 6 


845i 


85o6 


856i 


86i5 


8670 


55 


792 


8725 


8780 


8835 


8890 


8944 


8999 


9054 


9109 


9164 


9218 


55 


7 9 3 


9273 


9328 


9 383 


9437 


9492 


9 547 


9602 


9 656 


9711 


9766 


55 


794 


#9821 


9875 


9930 


9985 


♦039 


0094 


0149 


0203 


0258 


03l2 


55 


79 5 


90 0367 


0422 


0476 


o53i 


o586 


0640 


0695 


0749 


0804 


o85 9 


55 


796 


0913 


0968 


1022 


1077 


ii3i 


1 186 


1240 


1295 


1 349 


1404 


55 


797 


1458 


i5i3 


i56 7 


1622 


1676 


1731 


i 7 85 


1840 


1894 


1948 


54 


798 


2003 


2057 


2112 


2166 


2221 


2275 


2329 


2384 


2438 


2492 


54 


799 


2547 


2601 


2655 


2710 


2764 


2818 


2873 


2927 


2981 


3o36 


54 


800 


3090 


3i44 


3199 


3253 


3307 


336i 


34i6 


3470 


3524 


3578 


54 | 


801 


3633 


368 7 


3741 


3795 


3849 


3904 


3 9 58 


4012 


4066 


4120 


54 


802 


4i74 


4229 


4283 


433 7 


43gi 


4445 


4499 


4553 


4607 


4661 


54 


8o3 


4716 


4770 


4824 


4878 


4932 


4986 


5o4o 


5094 


5i48 


5202 


54 


804 


5256 


53io 


5364 


54i8 


5472 


5526 


558o 


5634 


5688 


5742 


54 


8o5 


5796 


585o 


5904 


5 9 58 


6012 


6066 


6119 


6173 


6227 


628l 


54 


806 


6335 


638 9 


6443 


6497 


655i 


6604 


6658 


6712 


6766 


6820 


54 


807 


6874 


6927 


6981 


7o35 


7089 


7i43 


7196 


725o 


73o4 


7358 


54 


808 


74u 


7465 


7619 


7573 


7626 


7680 


7734 


7787 


7841 


7895 


54 


809 


7949 


8002 


8o56 


8110 


8i63 


8217 


8270 


8324 


8378 


843 1 


54 


810 


8485 


853 9 


85 9 2 


8646 


8699 


8 7 53 


8807 


8860 


8914 


8967 


54 


811 


9021 


9074 


9128 


9181 


9 235 


9289 


9342 


9396 


9449 


90o3 


54 


812 


# 9556 


9610 


9663 


9716 


9770 


9823 


9877 


9930 


9984 


♦037 


53 l 


8i3 


91 OO9I 


0144 


0197 


025l 


o3o4 


o358 


0411 


0464 


o5i8 


0571 


53 


814 


0624 


0678 


0731 


0784 


o838 


0891 


0944 


0998 


io5i 


1 1 04 


53 


8i5 


n58 


1211 


1264 


1317 


1371 


1424 


1477 


i53o 


1 584 


i63 7 


53 


816 


1690 


1743 


1797 


i85o 


1903 


1956 


2009 


2o63 


2116 


2169 


53 


817 


2222 


2275 


2328 


238i 


2435 


2488 


254i 


2594 


2647 


2700 


53 ! 


818 


2753 


2806 


2859 


2913 


2966 


3019 


3072 


3i25 


3178 


323i 


53 ! 


819 


3284 


3337 


3390 


3443 


3496 


3549 


36o2 


3655 


3708 


3761 


53 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


* 




14 




LOGARITHMS OF NUMBERS. Tabie I. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


D. 


820 


91 38i4 


386 7 


3920 


3973 


4026 


4079 


4i32 


4184 


4237 


4290 


53 


821 


4343 


4396 


4449 


45o2 


4555 


4608 


4660 


47i3 


4766 


4819 


53 


822 


4872 


4925 


4977 


5o3o 


5o83 


5i36 


5i8 9 


524i 


5294 


5347 


53 


823 


5400 


5453 


55o5 


5558 


56u 


5664 


5716 


5769 


5822 


5875 


53 


824 


5927 


5980 


6o33 


6o85 


6i38 


6191 


6243 


6296 


6349 


6401 


53 


825 


6454 


65o7 


655o 


6612 


6664 


6717 


6770 


6822 


68 7 5 


6927 


53 


826 


6980 


7o33 


7085 


7i38 


7190 


7243 


7295 


7348 


74oo 


7453 


53 


827 


7606 


7 558 


7611 


7663 


7716 


7768 


7820 


7873 


7925 


7978 


52 


828 


8o3o 


8o83 


8i35 


8188 


8240 


8293 


8345 


83 9 7 


845o 


85o2 


52 


829 


8555 


8607 


865 9 


8712 


8764 


8816 


8869 


8921 


8973 


9026 


52 


83o 


9078 


9i3o 


9 i83 


9235 


9287 


9340 


9392 


9444 


9496 


9549 


52 


83 1 


•x-9601 


9 653 


9706 


97 58 


9810 


9862 


9914 


9967 


♦019 


0071 


52 


832 


92 0123 


0176 


0228 


0280 


o332 


o384 


0436 


0489 


o54i 


0593 


52 


833 


0645 


0697 


0749 


0801 


o853 


0906 


o 9 58 


1010 


1062 


1114 


52 


834 


1 166 


1218 


1270 


l322 


i3 7 4 


1426 


1478 


i53o 


i582 


1 634 


52 


835 


1686 


1738 


1790 


1842 


1894 


1946 


1998 


2o5o 


2102 


2i54 


52 


•836 


2206 


2258 


23lO 


2362 


24U 


2466 


25i8 


2570 


2622 


2674 


52 


837 


2725 


2777 


2829 


2881 


2933 


2 9 85 


3o37 


3o8 9 


3 140 


3192 


52 


838 


3244 


3296 


3348 


3399 


345 1 


35o3 


3555 


3607 


3658 


3710 


52 1 


839 


3762 


38i4 


3865 


3917 


3969 


4021 


4072 


4124 


4176 


4228 


52 


840 


4279 


433 1 


4383 


4434 


4486 


4538 


458 9 


4641 


4693 


4744 


52 


841 


4796 


4848 


4899 


4951 


5oo3 


5o54 


5io6 


5i5 7 


5209 


5261 


52 


842 


53i2 


5364 


54i 5 


5467 


55i8 


5570 


5621 


5673 


5726 


5776 


52 


843 


5828 


5879 


5931 


5982 


6o34 


6o85 


6137 


6188 


6240 


6291 


5i 


844 


6342 


6394 


6445 


6497 


6548 


6600 


665 1 


6702 


6754 


68o5 


5i 


845 


6857 


6908 


6959 


701 1 


7062 


7ii4 


7i65 


7216 


7268 


7319 


5i 


846 


7370 


7422 


7473 


7524 


7576 


7627 


7678 


7 7 3o 


7781 


7832 


5i 


847 


7883 


7 9 35 


7986 


8037 


8088 


8140 


8191 


8242 


82 9 3 


8345 


5i 


848 


83 9 6 


8447 


8498 


8549 


8601 


8652 


8 7 o3 


8 7 54 


88o5 


885 7 


5i 


849 


8908 


8 9 5 9 


9010 


9061 


9112 


9163 


9215 


9266 


9317 


9 368 


5i 


85o 


9419 


9470 


9521 


9572 


9623 


9674 


9725 


9776 


9827 


9879 


5i 


85i 


* 9930 


9981 


♦032 


oo83 


oi34 


oi85 


0236 


0287 


o338 


o38 9 


5i 


852 


93 0440 


0491 


o542 


0592 


o643 


0694 


0745 


0796 


0847 


0898 


5i 


853 


0949 


1000 


io5i 


1102 


n53 


1204 


1254 


i3o5 


i356 


1407 


5! 


854 


1458 


1 509 


i56o 


1610 


1661 


1712 


1763 


1814 


1 865 


1915 


5i 


855 


1966 


2017 


2068 


2118 


2169 


2220 


2271 


2322 


2372 


2423 


5i 


856 


2474 


2524 


2575 


2626 


2677 


2727 


2778 


2829 


2879 


2930 


5i 


85 7 


2981 


3o3i 


3o82 


3i33 


3i83 


3234 


3285 


3335 


3386 


3437 


5i 


858 


3487 


3538 


358 9 


363 9 


3690 


374o 


3791 


384i 


38 9 2 


3 9 43 


5i 


85 9 


3993 


4o44 


4094 


4i45 


4195 


4246 


4296 


4347 


4397 


4448 


5i 


860 


4498 


4549 


4599 


465o 


4700 


475i 


4801 


4852 


4902 


4953 


5o 


861 


5oo3 


5o54 


5io4 


5i54 


52o5 


5255 


53o6 


5356 


54o6 


5457 


5o 


862 


55o7 


5558 


56o8 


5658 


5709 


5759 


58o 9 


586o 


5910 


5960 


5o 


863 


601 1 


6061 


6111 


6162 


6212 


6262 


63i3 


6363 


641 3 


6463 


5o 


864 


65i4 


6564 


6614 


6665 


671D 


6765 


68i5 


6865 


6916 


6966 


5o 


865 


7016 


7066 


7117 


7167 


7217 


7267 


73i 7 


7 36 7 


74i8 


7468 


5o 


866 


7618 


7 568 


7618 


7668 


.7718 


7769 


7819 


7869 


7919 


7969 


5o 


867 


8019 


8069 


8119 


8169 


8219 


8269 


8320 


8370 


8420 


8470 


5o 


868 


8520 


8570 


8620 


8670 


8720 


8770 


8820 


8870 


8920 


8970 


5o 


869 


9020 


9070 


9120 


9170 


9220 


9270 


9320 


9369 


9419 


9469 


5o 


870 


95io 


9569 


9619 


9669 


9719 


9769 


9819 


9869 


9918 


9968 


5o 


871 


940018 


0068 


0118 


0168 


0218 


0267 


o3i7 


0367 


0417 


0467 


5o 


872 


o5i6 


o566 


0616 


0666 


0716 


0765 


o8i5 


o865 


0915 


0964 


5o 


8 7 3 


1014 


1064 


1 1 14 


n63 


I2l3 


1263 


i3i3 


i362 


1412 


1462 


5o 


874 


i5n 


i56i 


161 1 


1660 1 1710 


1760 


1809 


i85g 


1909 


i 9 58 


5o 


8 7 5 


2008 


2o58 


2107 


2157 


2207 


2256 


23o6 


2355 


24o5 


2455 


5o 


876 


25o4 


2554 


26o3 


■2653 


2702 


2752 


2801 


285i 


2901 


2950 


5o 


877 


3ooo 


3o49 


3099 


3i48 


3198 


3247 


3297 


3346 


3396 


3445 


49 


878 


3495 


3544 


35g3 


3643 


3692 


3742 


3 79 i 


384i 


3890 3939 


49 


87Q 


3 9 8 9 


4o38 


4088 
2 


4i3 7 
3 


4186 


4236 


4285 


4335 


4384 4433 


49 


K 





1 


4 


5 


6 


7 


8 


9 



Table I. 


LOGARITHMS OF NUMBERS. 15 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


D. 


880 


94 4483 


4532 


458i 


463 1 


4680 


4729 


4779 


4828 


4877 


4927 


49 


881 


4976 


5o25 


5074 


5i24 


5i73 


5222 


5272 


532i 


5370 


5419 


49 


882 


5469 


55i8 


556 7 


56i6 


5665 


57l5 


5764 


58i3 


5862 


5912 


49 


883 


5961 


6010 


6059 


6108 


6i5 7 


6207 


6256 


63o5 


6354 


64o3 


49 


884 


6432 


65oi 


655i 


6600 


6649 


6698 


6747 


6796 


6845 


6894 


49 


885 


6943 


6992 


7041 


7090 


7U0 


7189 


7238 


7287 


7336 


7385 


49 


886 


7434 


7483 


7532 


7 58i 


763o 


7679 


7728 


7777 


7826 


7875 


49 


887 


7924 


797 3 


8022 


8070 


8119 


8l68 


8217 


8266 


83i5 


8364 


49 


888 


84i3 


8462 


85u 


856o 


8609 


8657 


8706 


8755 


8804 


8853 


49 


889 


8902 


8 9 5i 


8999 


9048 


9097 


9146 


9 i 9 5 


9244 


9292 


934i 


49 


890 


9390 


9439 


9488 


9536 


9585 


9634 


9683 


973i 


978o 


9829 


49 


891 


#9878 


9926 


9975 


♦024 


0073 


0121 


0170 


0219 


0267 


o3i6 


49 


892 


95 o365 


0414 


0462 


o5u 


o56o 


0608 


0657 


0706 


0754 


o8o3 


49 


8 9 3 


08 5 1 


0900 


0949 


0997 


1046 


1095 


1 143 


1192 


1240 


1289 


49 


894 


i338 


i386 


1435 


1483 


i532 


i58o 


1629 


1677 


1726 


1775 


49 


8 9 5 


1823 


1872 


1920 


i960 


2017 


2066 


2114 


2i63 


2211 


2260 


48 


896 


23o8 


2356 


24o5 


2453 


2502 


255o 


2599 


2647 


2696 


2744 


48 


897 


2792 


2841 


2889 


2 9 38 


2986 


3o34 


3o83 


3i3i 


3i8o 


3228 


48 
48 


898 


3276 


3325 


3373 


3421 


3470 


35i8 


3566 


36i5 


3663 


37 1 1 


899 


3760 


38o8 


3856 


3905 


3953 


4001 


4049 


4098 


4146 


4194 


48 


900 


4243 


4291 


433 9 


438 7 


4435 


4484 


4532 


458o 


4628 


4677 


48 


901 


4725 


4773 


4821 


4869 


4918 


4.966 


5oi4 


5o62 


5uo 


5i58 


48 


902 


5207 


5255 


53o3 


535i 


53g9 


5447 


5495 


5543 


5592 


564o 


48 


903 


5688 


5 7 36 


5784 


5832 


588o 


5928 


5976 


6024 


6072 


6120 


48 


904 


6168 


6216 


6265 


63i3 


636i 


6409 


6457 


65o5 


6553 


6601 


48 


905 


6649 


6697 


6745 


6 79 3 


6840 


6888 


6 9 36 


6984 


7032 


7080 


48 


906 


7128 


7176 


7224 


7272 


7320 


7368 


74i6 


7464 


7512 


7 55 9 


48 


907 


7607 


7655 


7703 


775i 


7799 


7847 


7894 


7942 


7990 


8o38 


48 


908 


8086 


8i34 


8181 


8229 


8277 


8325 


8373 


8421 


8468 


85i6 


48 


909 


8564 


8612 


865 9 


8707 


8755 


88o3 


885o 


8898 


8946 


8994 


48 


910 


9041 


9089 


9137 


9i85 


9232 


9280 


9328 


9375 


9423 


9471 


48 


911 


9318 


9566 


9614 


9661 


9709 


9757 


9804 


9 852 


9900 


9947 


48 


912 


* 9995 


♦042 


0090 


oi38 


oi85 


0233 


0280 


o328 


0376 


0423 


48 


913 


96 047 1 


o5i8 


o566 


o6i3 


0661 


0709 


0756 


0804 


o85i 


0899 


48 


- 914 


0946 


0994 


1 041 


1089 


n36 


1 184 


I23l 


1279 


i326 


1374 


47 


9i5 


1421 


1469 


i5i6 


1 563 


1611 


i658 


1706 


1753 


1801 


1848 


47 


916 


1895 


1943 


1990 


2o38 


2085 


2l32 


2180 


2227 


2275 


2322 


47 


917 


2369 


2417 


2464 


25ll 


2559 


2606 


2653 


2701 


2748 


2795 


47 


918 


2843 


2890 


2937 


2985 


3o32 


3079 


3i26 


3174 


3221 


3268 


47 


919 


33i6 


3363 


3410 


3457 


35o4 


3552 


3599 


3646 


36 9 3 


3741 


47 


920 


3 7 88 


3835 


3882 


3929 


3977 


4024 


4071 


4118 


4i65 


4212 


47 


921 


4260 


43o7 


4354 


4401 


4448 


4495 


4542 


4590 


463 7 


4684 


47 


922 


473i 


4778 


4825 


4872 


4919 


4966 


5oi3 


5o6i 


5io8 


5i55 


47 


923 


5202 


5249 


5296 


5343 


5390 


5437 


5484 


553i 


5578 


5625 


47 


924 


5672 


5719 


5 7 66 


58i3 


586o 


5907 


5954 


6001 


6048 


6095 


47 


925 


6l42 


6i8q 


6236 


6283 


6329 


63 7 6 


6423 


6470 


65i7 


6564 


47 


926 


66l I 


6658 


6705 


6752 


6799 


6845 


6892 


6 9 3o 


6986 


7o33 


47 


927 


7080 


7127 


7173 


7220 


7267 


73i4 


736i 


7408 


7454 


poi 


47 


928 


7548 


75 9 5 


7642 


7688 


77 35 


7782 


7829 


7875 


7922 


7969 


47 


929 


8016 


8062 


8109 


8i56 


8203 


8249 


8296 


8343 


83 9 o 


8436 


47 


93o 


8483 


853o 


85 7 6 


8623 


8670 


8716 


8763 


8810 


8856 


8 9 o3 


47 


93 1 


8 9 5o 


8996 


9043 


9090 


9i36 


9i83 


9229 


9276 


9323 


9369 


47 


932 


94i6 


9463 


95oo 


9556 


9602 


9649 


9695 


9742 


9789 


9 835 


47 


933 


#9882 


9928 


9975 


♦021 


0068 


0114 


0161 


0207 


0254 


o3oo 


47 


934 


97 o347 


0393 


0440 


0486 


o533 


0579 


0626 


0672 


0719 


0765 


46 


9 35 


0812 


o858 


0904 


0951 


0997 


1044 


1090 


1 137 


ii83 


1229 


46 


9 36 


1276 


l322 


1369 


I4i5 


1461 


i5o8 


1 554 


1 60 1 


1647 


i6q3 


46 


9 h 


1740 


I786 


i832 


1879 


1925 


1971 


2018 


2064 


2110 


2167 


46 


9 38 


2203 


2249 


2295 


2342 


2388 


2434 


2481 


2527 


2573 


2619 


46 


9 3 9 


2666 


2712 


2758 


2804 


285i 


2897 


2943 


2989 


3o35 3o82 


46 


N. 





1 





3 


4 


5 


6 


7 


8 


9 


D. 1 



16 




LOGARITHMS OF NUMBERS. Table I. 


Hi 





1 


2 


3 


4 


5 


6 


1 


8 


9 


D. 


940 


97 3i28 


3i 7 4 


3220 


3266 


33i3 


3359 


34o5 


345i 


3497 


3543 


46 


941 


3590 


3636 


3682 


3728 


3774 


3820 


3866 


3913 


3959 


4oo5 


46 


942 


4o5i 


4097 


4i43 


4189 


4235 


4281 


4327 


4374 


4420 


4466 


46 


943 


45i2 


4558 


4604 


46D0 


4696 


4742 


4788 


4834 


4880 


4926 


46 


944 


4972 


5oi8 


5o64 


5uo 


5i56 


5202 


5248 


5294 


534o 


5386 


46 


945 


5432 


5478 


5524 


5570 


56i6 


5662 


5707 


5 7 53 


5 799 


5845 


46 


946 


58 9 i 


5 9 37 


5 9 83 


6029 


6075 


6121 


6167 


6212 


6258 


63o4 


46 


947 


63 5o 


6396 


6442 


6488 


6533 


6579 


6625 


6671 


6717 


6763 


46 


948 


6808 


6854 


6900 


6946 


6992 


7037 


7083 


7129 


7175 


7220 


46 


949 


7266 


7312 


7358 


74o3 


7449 


7495 


754i 


7586 


7632 


7678 


46 


95o 


7724 


7769 


7815 


7861 
83i7 


7906 


79 52 


7998 


8o43 


8089 


8i35 


46 


95i 


8181 


8226 


8272 


8363 


8409 


8454 


85oo 


8546 


85 9 i 


46 


952 


863 7 


8683 


8728 


8774 


8819 


8865 


891 1 


8 9 56 


9002 


9047 


46 


9 53 


9093 


9i38 


9184 


923o 


9275 


9321 


9 366 


9412 


9 45 7 


95o3 


46 


954 


9548 


9594 


9639 


9 685 


97 3o 


9776 


9821 


9867 


9912 


99 58 


46 


9 55 


98 ooo3 


0049 


0094 


0140 


oi85 


023l 


0276 


0322 


0367 


0412 


45 


956 


o458 


o5o3 


0549 


0594 


0640 


o685 


0730 


0776 


0821 


0867 


45 


957 


0912 


0957 


ioo3 


1048 


1093 


1139 


1 184 


1229 


1275 


l320 


45 


9 58 


1 366 


1411 


1456 


i5oi 


1 547 


1592 


1637 


1 683 


1728 


1773 


45 


9 5 9 


1819 


1864 


1909 


1954 


2000 


2o45 


2090 


2i35 


2181 


2226 


45 


960 


2271 


23i6 


2362 


2407 


2452 


2497 


2543 


2588 


2633 


2678 


45 


961 


2723 


2769 


2814 


285 9 


2904 


2949 


2994 


3o4o 


3o85 


3i3o 


45 


962 


3175 


3220 


3265 


33io 


3356 


3401 


3446 


3491 


3536 


358i 


45 


9 63 


3626 


36 7 I 


3716 


3762 


3807 


3852 


38 97 


3942 


3987 


4o32 


45 


964 


4077 


4122 


4167 


4212 


4257 


43o2 


4347 


4392 


4437 


4482 


45 


9 65 


4527 


4572 


4617 


4662 


4707 


4752 


4797 


4842 


4887 


4932 


45 


966 


4977 


5022 


5067 


5lI2 


5i5 7 


5202 


5247 


5292 


5337 


5382 


45 


967 


5426 


5471 


55i6 


556i 


56o6 


565 1 


5696 


574i 


5786 


583o 


45 


968 


5875 


5920 


5 9 65 


6010 


6o55 


6100 


6i44 


6189 


6234 


6279 


45 


969 


6324 


636 9 


64i3 


6458 


65o3 


6548 


65 9 3 


6637 


6682 


6727 


45 


970 


6772 


6817 


6861 


6906 
7 353 


6951 


6996 


7040 


7o85 


7i3o 


7175 


45 


971 


7219 


7264 


7 3o 9 


7 3 9 8 


7443 


7488 


7532 


7577 


7622 


45 


972 


7666 


771.1 


7706 


7800 


7845 


7890 


79 34 


7979 


8024 


8068 


45 


973 


8u3 


8157 


8202 


8247 


8291 


8336 


838i 


8425 


8470 


85i4 


45 


974 


855 9 


8604 


8648 


86 9 3 


8737 


8782 


8826 


8871 


8916 


8960 


45 


97 5 


9005 


9049 


9094 


9»38 


9 i83 


9227 


9272 


9316 


936i 


94o5 


45 


976 


945o 


9494 


9 53 9 


9 583 


9628 


9672 


9717 


9761 


9806 


9 85o 


44 


977 


* 9895 


99 3 9 


99 83 


♦028 


0072 


0117 


0161 


0206 


0250 


0294 


44 


978 


99 o339 


o383 


0428 


0472 


o5i6 


o56i 


o6o5 


o65o 


0694 


0738 


44 


979 


0783 


0827 


0871 


0916 


0960 


1004 


1049 


1093 


1137 


1182 


44 


980 


1226 


1270 


i3i5 


1359 


i4o3 


1448 


1492 


1 536 


i58o 


1625 


44 


981 


1669 


1713 


1758 


1802 


1846 


1890 


1935 


1979 


2023 


2067 


44 


982 


21 1 1 


2 1 56 


2200 


2244 


2288 


2333 


2377 


2421 


2465 


2509 


44 


9 83 


2554 


25g8 


2642 


2686 


2730 


2774 


2819 


2863 


2907 


2951 


44 


984 


2995 


3o39 


3o83 


3127 


3172 


32i6 


326o 


33o4 


3348 


3392 


44 


9 85 


3436 


348o 


3524 


3568 


36i3 


3657 


3701 


3 7 45 


3789 


3833 


44 


986 


38 77 


3921 


3 9 65 


4009 


4o53 


4097 


4i4i 


4i85 


4229 


4273 


44 


987 


43i7 


436i 


44o5 


4449 


4493 


4537 


458 1 


4625 


4669 


47i3 


44 


988 


4757 


4801 


4845 


4889 


4933 


4977 


5021 


5o65 


5io8 


5i52 


44 


989 


5196 


524o 


5284 


5328 


5J72 


5416 


5460 


55o4 


5547 


5591 


44 


990 


5635 


56 79 


5723 


5767 


58n 


5854 


5898 


5942 


5 9 86 


6o3o 


44 


991 


6074 


6117 


6161 


6205 


6249 


6293 


6337 °38o 


6424 


6468 


44 


992 


65i2 


6555 


6599 


6643 


6687 


6731 


6774 


6818 


6862 


6906 


44 


99 3 


6949 


6993 


7037 


7080 


7124 


7168 


7212 


7255 


7299 


7343 


44 


994 


7386 


743o 


7474 


7517 


756i 


7605 


7648 


7692 


7736 


7779 


44 


99 5 


7823 


7867 


7910 


7 9 54 


7998 


8041 


8o85 


8129 


8172 


8216 


44 


996 


825 9 


83o3 


8347 


83 9 o 


8434 


8477 


852i 


8564 


8608 


8652 


44 


997 


8690 


8739 


8782 


8826 


8869 


8 9 i3 


8956 


9000 


9043 


9087 


44 


998 


9i3i 


9H4 


9218 


9261 


93o5 


9 348 


9 3 9 2 


9435 


9479 


9522 


44 


999 


9 565 


9609 


9652 


9696 
3 


9739 


97 83 


9826 


9870 


99 i3 


9957 


43 
D. 


N. 





1 





4 


5 


6 


1 


8 


9 



TABLE II. 



LOGARITHMIC SINES AND TANGENTS, 



FOR 



EVERY DEGREE AND MINUTE OF THE QUADRANT. 



If the logarithms of the values in Table III. be each increased by 10, the results 
will be the values of this table. 

The logarithmic Secants and Cosecants are not given. They may be readily ob- 
tained, as follows: — Subtract the logarithmic Cosine from 20, and the remainder 
will be the logarithmic Secant ; subtract the logarithmic Sine from 20, and the 
remainder will be the logarithmic Cosecant. 



18 


LOGARITHMIC SINES, 


TANGENTS, ETC 


Table 


II. 


0° 














179° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


1 





Inf. Neg. 




10-000000 




Inf. Neg. 




Infinite. 


60 


i 


6-463726 


501717 


000000 


00 


6-463726 


501717 


i3- 536274 


5 9 


2 


764756 


293485 


000000 


00 


764756 


293483 


235244 


58 


3 


94o847 


20823l 


000000 


00 


940847 


2o823i 


059 1 53 


57 


4 


7-065786 


161517 


000000 


00 


7-065786 


161517 


12-934214 


56 


5 


162696 


i3io68 


000000 


00 


162696 


i3io6o 


8373o4 


55 


6 


241877 


111075 


9-999999 


01 


241878 


1 1 1678 


758122 


54 


7 


3o8824 


o6653 


999999 


01 


3o8825 


99653 


691175 


53 


8 


3668i6 


85254 


999999 


01 


366817 


83254 


633i83 


52 


9 


417968 


76263 


999999 


01 


417970 


76263 


582o3o 


5i 


10 


463726 


68988 


999998 


01 


463727 


68988 


536273 


5o 


ii 


7-5o5n8 


62981 


9.999998 


01 


7-5o5i2o 


62981 


12-494880 


4o 


12 


542906 


57936 


999997 


01 


542909 


57933 


467091 


48 


i3 


577668 


53641 


999997 


01 


577672 


53642 


422328 


47 


i4 


609853 


49938 


999996 


01 


609857 


49939 


390143 


46 


i5 


63 9 8i6 


467U 


999996 


01 


639820 


46715 


36oi8o 


45 


16 


667845 


4388i 


99999 5 


01 


667849 


43882 


332i5i 


44 


17 


694173 


41372 


999995 


01 


694179 


4i373 


3o582i 


43 


18 


718997 


39135 


999994 


01 


719003 


39136 


280997 


42 


19 


742478 


37127 


999993 


01 


742484 


37128 


257616 


4i 


20 


764754 


353i5 


999993 


01 


764761 


35i36 


236239 


4o 


21 


7-785943 


33672 


9.999992 


01 


7-785951 


33673 


12-214049 


39 


22 


806146 


32175 


999991 


01 


8061 55 


32176 


193846 


38 


23 


82545i 


3o8o5 


999990 


01 


825460 


3o8o6 


174540 


37 


U 


843934 


29547 


999989 


02 


843944 


29549 


166066 


36 


25 


861662 


28388 


999989 


02 


861674 


28390 


138326 


35 


26 


878695 


27317 


999988 


02 


878708 


27318 


121292 


34 


27 


895085 


26323 


999987 


02 


895099 


26325 


1 0490 1 


33 


28 


910879 


25399 


999986 


02 


910894 


254oi 


089106 


32 


29 


926119 


24538 


999985 


02 


926134 


2454o 


073866 


3i 


3o 


940842 


23 7 33 


999983 


02 


94o858 


23735 


069142 


3o 


3i 


7-955082 


22980 


9.999982 


02 


7-955ioo 


22981 


1 2 • 044900 


29 


32 


968870 


22273 


999981 


02 


968889 


22275 


o3 1 1 1 1 


28 


33 


982233 


21608 


999980 


02 


982253 


21610 


017747 


27 


34 


995198 


20981 


999979 


02 


995219 


20983 


004781 


26 


35 


8-007787 


20390 


999977 


02 


8-007809 


20392 


11-992191 


25 


36 


020021 


1 983 1 


999976 


02 


020044 


i 9 833 


979956 


24 


37 


o3ioi9 


19302 


999975 


02 


031945 


19305 


968055 


23 


38 


o435oi 


18801 


999973 


02 


043627 


i88o3 


956473 


22 


3 9 


064781 


18325 


999972 


02 


054809 


18327 


945191 


21 


4o 


065776 


17872 


999971 


02 


o658o6 


17874 


934194 


20 


4i 


8-076500 


1 744i 


9.999969 


02 


8-076531 


17444 


11-923469 


ID 


42 


o86 9 65 


1703 1 


999968 


02 


086997 


17034 


9i3oo3 


10 


43 


097183 


i663o 


999966 


02 


097217 


16642 


902783 


17 


44 


107167 


16265 


999964 


o3 


10720a 


16268 


892797 
883 037 


16 


45 


1 16926 


15908 


999963 


o3 


n6 9 63 


15910 


i5 


46 


1 2647 1 


1 5566 


999961 


o3 


126610 


1 5568 


873490 


14 


47 


i358io 


i5238 


999959 


o3 


i3585i 


i524i 


864149 


i3 


48 


144953 


14924 


9 999 58 


o3 


144996 


14927 


855oo4 


12 


49 


153907 


14622 


999956 


o3 


1539D2 


14627 


846048 


11 


5o 


162681 


14333 


999954 


o3 


162727 


14336 


837273 


10 


5i 


8-171280 


1 40 54 


9-999952 


o3 


8-171328 


14057 


11-828672 


9 


52 


i797i3 


13786 


99995o 


o3 


179763 


13790 


820237 


8 


53 


187985 


13529 


999948 


o3 


i88o36 


i3532 


811964 


7 


54 


196102 


i328o 


999946 


o3 


196156 


13284 


8o3844 


6 


55 


204070 


i3o4i 


999944 


o3 


204126 


i3o44 


7958 7 4 


5 


56 


211895 


12810 


999942 


04 


211953 


12814 


788047 


4 


5 7 


219581 


12587 


999940 


04 


219641 


12590 


78o35q 


3 


58 


227134 


12372 


999938 


04 


227195 


12376 


772806 


2 


5 9 


234557 


12 164 


999936 


04 


234621 


12168 


765379 


1 


60 


24i855 


1 1963 


999934 


04 


241921 


1 1 967 


758079 





/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


/ 


90 c 


► 














89° 



Table II. 


LOGARITHMIC 


SINES, TANGENTS, ETC. 


19 


1° 














178° 


r 


Sine. 


D. 


Cosine. 


Id. 


Tang. 


D. 


Cotang. 


60 





8-24i855 


1 1963 


9-999934 


04 


8-241921 


1 1967 


II.758079 


i 


249033 


11768 


99 99 32 


04 


249102 


11772 


750898 


5 9 


2 


256094 


li58o 


999929 


04 


256i65 


1 1 584 


743835 


58 


3 


263o42 


1 1 398 


999927 


04 


263n5 


1 1402 


736885 


57 


4 


269881 


11221 


999925 


04 


269956 


II225 


730044 


56 


5 


276614 


no5o 


999922 


04 


276691 


no54 


723309 


55 


6 


283243 


io883 


999920 


04 


283323 


10887 


716677 


54 


7 


289773 


10721 


999918 


04 


289806 


10726 


710144 


53 


8 


296207 


io565 


999915 


04 


296292 


10670 


703708 


52 


9 


3o2546 


io4i3 


999913 


04 


302634 


10418 


697366 


5i 


10 


308794 


10266 


999910 


04 


3o8884 


10270 


691116 


5o 


it 


8> 314954 


10122 


9.999907 


04 


8-3i5o46 


10126 


11-684954 


4Q 


12 


321027 


9982 


999905 


04 


32II22 


99g7 


678878 


48 


i3 


327016 


9847 


999902 


04 


327114 


985i 


672886 


47 


14 


332924 


97U 


999899 


o5 


333o25 


9719 


666975 


46 


i5 


338 7 53 


9 586 


999897 


o5 


338856 


9590 


661 144 


45 


16 


3445o4 


9460 


999894 


o5 


344610 


9465 


655390 


44 


17 


35oi8i 


9 338 


999891 


o5 


360289 


9 343 


6497 1 1 


43 


18 


355 7 83 


9219 


999888 


o5 


3558o5 


9224 


644105 


42 


l 9 


36i3i5 


oio3 


999885 


o5 


36i43o 


9108 


638570 


4i 


20 


366777 


8990 


999882 


o5 


3668 9 5 


8 99 5 


633 1 o5 


4o 


21 


8-372171 


8880 


9.999879 


o5 


8-372292 


8885 


11-627708 


3 9 


22 


377499 


8772 


999876 


o5 


377622 


8777 


622378 


38 


23 


382762 


8667 


999873 


o5 


382889 


8672 


617111 


37 


24 


387962 


8564 


999870 


o5 


388092 


8570 


61 1908 


36 


25 


393101 


8464 


999867 


o5 


393234 


8470 


606766 


35 


26 


398179 


8366 


999864 


o5 


3 9 83i5 


83 7 i 


6oi685 


34 


27 


403199 


8271 


999861 


o5 


4o3338 


8276 


596662 


33 


28 


408161 


8177 


99 9 858 


o5 


4o83o4 


8182 


5oi6o6 


32 


29 


4i3o68 


8086 


999854 


o5 


4i32i3 


8091 


586787 


3i 


3o 


4i79 r 9 


7996 


999851 


06 


418068 


8002 


581932 


3o 


3i 


8-422717 


7909 


9-999848 


06 


8.422869 


79U 


n-577i3i 


29 


32 


427462 


7823 


999844 


06 


427618 


783o 


5 7 2382 


28 


33 


432i56 


7740 


999841 


06 


4323i5 


7745 


567685 


27 


34 


4368oo 


7 65 7 


9 99 838 


06 


436o62 


7663 


563o38 


26 


35 


44i394 


7577 


999834 


06 


44i 56o 


7 583 


558440 


25 


36 


445941 


7499 


99983 1 


06 


4461 10 


75o5 


5538 9 o 


24 


37 


45o44o 


7422 


999827 


06 


45o6i3 


7428 


549387 


23 


38 


454893 


7346 


999824 


06 


455070 


7352 


544q3o 


22 


3 9 


459301 


7273 


999820 


06 


459481 


7279 


54oo 1 9 


21 


4o 


463665 


7200 


999816 


06 


463849 


7206 


536i5i 


20 


4i 


8-467985 


7129 


9-999813 


06 


8-468172 


7i35 


ii-53i828 


io 


42 


472263 


7060 


999809 


06 


472454 


7066 


527546 


18 


43 


476498 


6991 


999806 


06 


476693 


6998 


523307 
519108 


17 


44 


480693 


6924 


999801 


06 


480892 


6 9 3i 


16 


45 


484848 


685 9 


999797 


07 


485oDo 


6865 


5i4g5o 


i5 


46 


488963 


6794 


999794 


07 


489170 


6801 


5io83o 


14 


47 


493040 


6 7 3 1 


999790 


07 


493260 


6738 


506750 


i3 


48 


497078 


6669 


999786 


07 


497293 


6676 


502707 


12 


49 


5oio8o 


6608 


999782 


07 


501298 


66i5 


498702 


11 


5o 


5o5o45 


6548 


999778 


°7 


5o5207 


6555 


494733 


10 


5i 


8.508974 


6489 


9-999774 


07 


8.509200 


6496 


ii-4qo8oo 





52 


512867 


6431 


999769 


07 


513098 


6439 


486902 


8 


53 


516726 


6375 


999765 


07 


516961 


6382 


483o39 


7 


54 


52o55i 


63 19 


999761 


07 


520790 


6326 


479210 


6 


55 


524343 


6264 


999737 


07 


524586 


6272 


476414 


5 


56 


528102 


6211 


999753 


07 


528349 


6218 


47i65i 


4 


5 7 


53i828 


6i58 


999748 


07 


532o8o 


6i65 


467920 


3 


58 


535523 


6106 


999744 


07 


535779 


6u3 


464221 


2 


5 9 


539186 


6o55 


999740 


07 


53 9 447 


6062 


46o553 


1 


60 


542819 


6004 


999735 


07 


543o84 


6012 


456916 





/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


/ 


91 c 














1 


}8° 



20 


LOGARITHMIC SINES, 


TANGENTS, ETC 


Table II. 


2° 














177° 


i 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


/ 





8-542819 


6004 


9.999735 


07 


8 .543o84 


6012 . 


II -456916 
4533o9 


60 


i 


546422 


5 9 55 


999731 


07 


546691 


5962 


5 9 


2 


549995 


5906 


999726 


07 


55o268 


5914 


449732 


58 


3 


553539 


5858 


999722 


08 


5538i7 


5866 


446 1 83 


57 


4 


557o54 


58n 


999717 


08 


557336 


58i 9 


442664 


56 


5 


56o54o 


5 7 65 


9997 1 3 


08 


560828 


5773 


439172 


55 


6 


563999 


5 7 i 9 


999708 


08 


564291 


5727 


435709 


54 


7 


56743i 


D674 


999704 


08 


567727 


5682 


432273 


53 


8 


570836 


563o 


999699 


08 


571137 


5638 


428863 


52 


9 


574214 


5587 


999694 


08 


574520 


55 9 5 


42548o 


5i 


10 


577566 


5544 


999689 


08 


577877 


5552 


422123 


5o 


ii 


8-58o8 9 2 


55o2 


9-999685 


08 


8.581208 


55io 


IW18792 


49 


12 


584193 


546o 


999680 


08 


5845i4 


5468 


4i54»6 


48 


i3 


587469 


5419 


999675 


08 


587795 


5427 


412205 


47 


U 


090721 


53 79 


999670 


08 


591061 


538 7 


408949 


46 


i'.5 


593948 


533 9 


999665 


08 


594283 


5347 


405717 


45 


16 


597162 


53oo 


999660 


08 


597492 


53o8 


402608 


44 


n 


6oo332 


5261 


999655 


08 


600677 


5270 


399323 


43 


18 


6o348o 


5223 


999650 


08 


6o383o 


5232 


396161 


42 


J 9 


606623 


5i86 


999645 


09 


606978 


5194 


393022 


41 


20 


609734 


5i4g 


999640 


09 


610094 


5i58 


389906 


4o 


21 


8-612823 


5lI2 


9-999635 


09 


8-6i3i8 9 


5l2I 


ii-3868ii 


39 


22 


6i58 9 i 


5076 


999629 


09 


616262 


5o85 


383738 


38 


23 


618937 


5o4i 


999624 


09 


619313 


5o5o 


380687 


37 


24 


621962 


5oo6 


999619 


09 


622343 


5oi5 


377657 


36 


25 


624965 


4972 


999614 


09 


625352 


4981 


374648 


35 


26 


627948 


4938 


999608 


09 


628340 


4947 


371660 


34 


27 


630911 


4904 


999603 


09 


63i3o8 


4913 


3686 9 2 


33 


28 


633854 


4871 


999597 


09 


634256 


4880 


365744 


32 


29 


636776 


483 9 


999592 


09 


637184 


4848 


362816 


3i 


3o 


63 9 68o 


4806 


999586 


09 


640093 


4816 


359907 


3o 


3i 


8-642563 


4775 


9.999581 


09 


8-642982 


4784 


11-357018 


29 


32 


645428 


4743 


999575 


09 


645853 


4753 


354i47 


28 


33 


648274 


4712 


999570 


09 


648704 


4722 


351296 


27 


34 


65no2 


4682 


999564 


09 


65i537 


4691 


348463 


26 


35 


653gi 1 


4652 


999558 


10 


654352 


4661 


345648 


25 


36 


656702 


4622 


999553 


10 


657149 


463 1 


34285i 


24 


37 


659475 


4592 


999547 


10 


659928 


4602 


340072 


23 


38 


66223o 


4563 


999541 


10 


662689 


45 7 3 


3373i 1 


22 


3 9 


664968 


4535 


999535 


10 


665433 


4544 


334567 


21 


4o 


667689 


45o6 


999529 


10 


668160 


4526 


33i84o 


20 


4i 


8-670393 


4479 


9-999024 


10 


8-670870 


4488 


n-329i3o 


IQ 


42 


673080 


445 1 


999518 


10 


673563 


446i 


326437 


l8 


43 


675751 


4424 


999512 


10 


676239 


4434 


323761 


17 


44 


678405 


4397 


999506 


10 


678900 


4417 


32IIOO 


16 


45 


68io43 


4370 


999500 


10 


68i544 


438o 


3 1 8456 


i5 


46 


683665 


4344 


999493 


10 


684172 


4354 


3i5828 


14 


47 


686272 


43i8 


999487 


10 


686784 


4328 


3i32i6 


i3 


48 


688863 


4292 


999481 


10 


689381 


43 o3 


310619 


12 


i 9 


691438 


4267 


999475 


10 


691963 


4277 


3o8o37 


11 


5o 


693998 


4242 


999469 


10 


694629 


4252 


3o547i 


IO 


5i 


8 -6 9 6543 


4217 


9-999463 


11 


8-697081 


4228 


11-302919 





52 


699073 


4192 


999456 


11 


699617 


42o3 ' 


3oo383 


8 


53 


701589 


4168 


99945o 


11 


702139 


4179 


297861 


7 


54 


704090 


4U4 


999443 


11 


704646 


4i55 


295354 


6 


55 


706577 


41 2 1 


999437 


11 


707140 


4i32 


292860 


5 


56 


709049 


4097 


99943i 


11 


709618 


4108 


290382 


4 


A 


711507 


4074 


999424 


11 


712083 


4o85 


287917 


3 


713952 


4o5i 


999418 


11 


714534 


4062 


285466 


2 


5 9 


7i6383 


4029 


99941 1 


11 


716972 


4o4o 


283028 


1 


60 


718800 


4006 


999404 


11 


719396 


4017 


280604 





t 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


r 


92 c 


> 












87° 



[ Table II. LOGARITHMIC SINES 


, TANGENTS, ETC. 


21 


3° 














176° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


1 





8-718800 


4006 


9-999404 


II 


8-719396 


4017 


II • 280604 


60 


i 


721204 


3984 


999398 


II 


721806 


3995 


278194 


5o 


2 


723595 


3962 


999391 


II 


724204 


3974 


275796 


58 1 


3 


725972 


3941 


999384 


11 


726588 


3902 


273412 


57 


4 


728337 


3919 


999378 


11 


728959 


393o 


271041 


56 


5 


730688 


3898 


999371 


11 


73i3i7 


3909 


268683 


55 


6 


733027 


38 77 


999364 


12 


733663 


388 9 


266337 


54 


7 


735354 


385 7 


999357 


12 


735996 


3868 


264004 


53 


8 


737667 


3836 


99935o 


12 


738317 


3848 


261683 


52 


9 


739969 


38i6 


999343 


12 


740626 


3827 


259374 


5i 


10 


742259 


3796 


99g336 


12 


742922 


3807 


257078 


5o 


ii 


8-744536 


3 77 6 


9.999329 


12 


8-745207 


3787 


11.254793 


4o 


12 


746802 


3756 


999322 


12 


747479 


3768 


2D252I 


48 


i3 


749055 


3 7 3 7 


9993 1 5 


12 


749740 


3749 


25o26o 


47 


i4 


751297 


3717 


999 3o8 


12 


751989 


3729 


24801 1 


46 


i5 


753528 


36 9 8 


999301 


12 


754227 


3710 


245773 


45 


16 


755747 


3679 


999294 


12 


756453 


3692 


243547 


44 


n 


757955 


366i 


999287 


12 


758668 


36 7 3 


24l332 


43 


18 


760151 


3642 


999279 


12 


760872 


3655 


239128 


42 


19 


762337 


3624 


999272 


12 


763o65 


3636 


236935 


4i 


20 


76451 1 


36o6 


999265 


12 


765246 


36i8 


234754 . 


4o 


21 


8.766675 


3588 


9.999257 


12 


8-767417 


36oo 


n-232583 


3 9 


22 


768828 


3570 


999250 


13 


769578 


3583 


23o422 


38 


23 


770970 


3553 


999242 


13 


771727 


3565 


228273 


37 


24 


773101 


3535 


999235 


i3 


773866 


3548 


226134 


36 


25 


775223 


35i8 


999227 


i3 


775995 


353i 


224005 


35 


26 


777333 


35oi 


999220 


i3 


7781U 


35i4 


221886 


34 


27 


779434 


3484 


999212 


i3 


780222 


3497 


219778 


33 


28 


781524 


3467 


999205 


i3 


782320 


348o 


217680 


32 


29 


7836o5 


345i 


999197 


i3 


784408 


3464 


215592 


3i 


3o 


785675 


343 1 


999189 


i3 


786486 


3447 


2i35i4 


3o 


3i 


8.787736 


34i8 


9-999181 


i3 


8.788554 


343 1 


11-211446 


29 


32 


789787 


3402 


999174 


i3 


790613 


34i4 


209387 


28 


33 


791828 


3386 


999166 


i3 


792662 


3399 


207338 


27 


34 


793859 


3370 


999 1 58 


i3 


794701 


3383 


206299 


26 


35 


795881 


3354 


999i5o 


i3 


796731 


3368 


203269 


25 


36 


797894 


3339 


999142 


i3 


798752 


3352 


201248 


24 


3? 


799897 


3323 


999134 


i3 


800763 


3337 


199237 


23 


38 


801892 


33o8 


999126 


i3 


802765 


3322 


197235 


22 


3 9 


803876 


3293 


9991 18 


i3 


8o4758 


3307 


196242 


21 


4o 


8o5852 


32 7 8 


999110 


i3 


806742 


3292 


193258 


20 


4i 


8-807819 


3263 


9.999102 


i3 


8-808717 


3278 


11-191283 


IO 


42 


809777 


3249 


999094 


14 


8io683 


3262 


1 893 1 7 


10 


43 


811726 


3234 


999086 


14 


81 2641 


3248 


187359 


17 


44 


8i366 7 


32IQ 


999077 


14 


8i458 9 


3233 


1 854i 1 


16 


45 


815599 


32o5 


999069 


14 


816529 


3219 


1 8347 1 


i5 


46 


817522 


3191 


999061 


14 


818461 


32o5 


i8i53 9 


14 


47 


8i 9 436 


3177 


999053 


14 


820384 


3191 


179616 


i3 


48 


821343 


3i63 


999044 


14 


822298 


3177 


177702' 


12 


49 


823240 


3i4g 


999036 


14 


824205 


3i63 


175795 


11 


5o 


825i3o 


3i35 


999027 


14 


826103 


3i5o 


173897 


10 


5i 


8-827011 


3l22 


9.999019 


14 


8-827992 


3i36 


11-172008 





52 


828884 


3io8 


999010 


14 


829874 


3i23 


170126 


8 


53 


830749 


3095 


999002 


14 


831748 


3no 


168252 


7 


54 


832607 


3o82 


998993 


14 


8336i3 


3096 


166387 


6 


55 


834456 


3069 


998984 


14 


835471 


3o83 


164529 


5 


56 


836297 


3o56 


998976 


14 


837321 


3070 


162679 


4 


5 7 


838i3o 


3o43 


998967 


i5 


839163 


3o57 


160837 


3 


58 


83 9 g56 


3o3o 


9 9 8 9 58 


i5 


840998 


3o45 


159002 


2 


5 9 


841774 


3017 


998950 


i5 


842825 


3o32 


157175 


1 


60 


843585 


3ooo 


998941 


i5 


844644 


3019 


155356 





/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


/ 


93 c 


> 














36° 



22 


LOGARITHMIC SINES, 


TANGENTS, ETC 


Table II. 


4° 














175° 


i 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


/ 





8-843585 


3oo5 


9-998941 


i5 


8-844644 


3019 


n-l55356 


60 


i 


845387 


2992 


998932 


i5 


846455 


3007 


i53545 


5 9 


2 


847183 


2980 


998923 


i5 


848260 


2995 


151740 


58 


3 


848971 


2967 


9989U 


i5 


85oo57 


2982 


U9943 


57 


4 


85o75i * 


2955 


998905 


ID 


85 1 846 


2970 


I48i54 


56 


5 


852525 


2943 


998896 


i5 


853628 


2 9 58 


146372 


55 


6 


854291 


2931 


998887 


i5 


8554o3 


2946 


144597 


54 


7 


856o49 


2919 


998878 


i5 


8D7171 


2935 


142829 


53 


8 


857801 


2907 


998869 


i5 


858 9 32 


2923 


141060 


52 


9 


85 9 546 


2896 


998860 


i5 


860686 


2911 


139314 


5i 


10 


86i283 


2884 


99 885i 


i5 


862433 


2900 


137567 


5o 


ii 


8-863oi4 


2873 


9-998841 


i5 


8-864173 


2888 


11 • i35827 


49 


12 


864738 


2861 


998832 


i5 


865906 


2877 


134094 


48 


i3 


866455 


285o 


998823 


16 


86 7 632 


2866 


132368 


47 


14 


868i65 


283g 


99 88i3 


16 


86 9 35i 


2854 


1 30649 


46 


i5 


869868 


2828 


998804 


16 


871064 


2843 


128 9 36 


45 


16 


87i565 


2817 


998795 


16 


872770 


2832 


127230 


44 


17 


873255 


2806 


998785 


16 


874469 


2821 


I2553i 


43 


18 


874938 


2795 


998776 


16 


876162 


2811 


123838 


42 


19 


876615 


2786 


998766 


16 


877849 


2800 


I22l5l 


41 


20 


878285 


2773 


998757 


16 


879529 


2789 


1 2047 1 


4o 


21 


8-879949 


2763 


9.998747 


16 


8-881202 


2779 


ii'ii8798 


3 9 


22 


881607 


2752 


998738 


16 


882869 


2768 


H7i3i 


38 


23 


883258 


2742 


998728 


16 


88453o 


2758 


1 1 5470 


37 


24 


884903 


2731 


998718 


16 


886i85 


2747 


n38i5 


36 


25 


886542 


2721 


998708 


16 


88 7 833 


2737 


112167 


35 


26 


888174 


2711 


998699 


16 


889476 


2727 


no524 


34 


27 


889801 


2700 


998689 


16 


891112 


2717 


108888 


33 


28 


891421 


2690 


998679 


16 


892742 


2707 


107258 


32 


29 


8 9 3o35 


2680 


998669 


17 


894366 


2697 


io5634 


3i 


3o 


894643 


2670 


998659 


17 


8 9 5 9 84 


2687 


104016 


3o 


3i 


8-896246 


2660 


9-998649 


n 


8-897596 


2677 


11-102404 


29 


32 


897842 


265i 


998639 


17 


899203 


2667 


100797 


28 


33 


899432 


2641 


998629 


17 


900803 


2658 


099197 


27 


34 


901017 


263 1 


998619 


17 


902398 


2648 


097602 


26 


35 


902596 


2622 


998609 


H 


903987 


2638 


096013 


25 


36 


904169 


2612 


998599 


*7 


905570 


2629 


094430 


24 


37 


906736 


26o3 


998589 


H 


907147 


2620 


092853 


23 


38 


907297 


25o3 


99 85 7 8 


17 


908719 


2610 


091281 


22 


3 9 


908853 


2584 


99 8568 


17 


910285 


2601 


089715 


21 


4o 


910404 


2575 


99 8558 


17 


91 1846 


2592 


088154 


20 


4i 


8-911949 


2566 


9-998548 


17 


8-9i34oi 


2583 


11-086599 


lO 


42 


913488 


2556 


998537 


17 


91 495 1 


2574 


o85o49 


l8 


43 


9l5o22 


2547 


998027 


17 


916495 


2565 


o835o5 


17 


44 


9i655o 


2538 


9985i6 


18 


918034 


2556 


081966 


16 


45 


918073 


2029 


998506 


18 


919568 


2547 


080432 


i5 


46 


919591 


2520 


998495 


18 


921096 


2538 


078904 


14 


47 


921103 


25l2 


998485 


18 


922619 


253o 


077381 


i3 


48 


922610 


25o3 


998474 


18 


924i36 


2521 


075864 


12 


i 9 


9241 1 2 


2494 


998464 


18 


925649 


25l2 


07435i 


11 


5o 


925609 


2486 


998453 


18 


927156 


25o3 


072844 


10 


5i 


8-927100 


2477 


9-998442 


18 


8-928658 


2495 


11-071342 





52 


928D87 


2469 


998431 


18 


93oi55 


2486 


060845 


8 


53 


930068 


2460 


998421 


18 


931647 


2478 


o68353 


7 


54 


93 1 544 


2452 


998410 


18 


933 i34 


2470 


066866 


6 


55 


933oi5 


2443 


998399 


18 


934616 


2461 


o65384 


5 


56 


934481 


2435 


99 8388 


18 


936093 


2453 


063907 


4 


57 


935942 


2427 


998377 


18 


937565 


2445 


062435 


3 


58 


937398 


2419 


998366 


18 


939032 


2437 


060968 


2 


5 9 


9 3885o 


241 1 


998355 


18 


940494 


243o 


o595o6 


1 


60 


940296 


24o3 


998344 


18 


941902 


2421 


o58o48 





r 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


/ 


94 c 














85° 



Table II. LOGARITHMIC SINES 


, TANGENTS, ETC. 


23 


5° 














174° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


/ 





8-040296 


24o3 


9-998344 


19 


8-941952 


2421 


ii-o58o48 


60 


i 


941738 


23g4 


99 8333 


19 


943404 


24i3 


056596 


5 9 


2 


943i74 


2387 


998322 


19 


944852 


24o5 


o55i48 


58 


3 


944606 


2379 


9983 1 1 


19 


946295 


2397 


o537o5 


57 


4 


946034 


2371 


998300 


19 


947734 


2390 


052266 


56 


5 


947456 


2363 


998289 


19 


949168 


2382 


o5o832 


55 


6 


948874 


2355 


998277 


19 


950597 


2374 


049403 


54 


7 


950287 


2348 


998266 


19 


952021 


2366 


047979 


53 


8 


951696 


234o 


998255 


19 


95344i 


236o 


046559 


52 


9 


953ioo 


2332 


998243 


19 


954856 


235i 


o45 1 44 


5i 


10 


954499 


2325 


998232 


IS 


956267 


2344 


043733 


5o 


ii 


8-955894 


23i7 


9-998220 


19 


8-957674 


2337 


11 .042326 


40 


12 

i3 


957284 
958670 


23l0 
2302 


998209 
998197 


19 
19 


959075 
960473 


2329 

2323 


040925 
039327 


48 
47 


U 


960062 


2295 


998186 


*9 


961866 


23i4 


o38i34 


46 


i5 


961429 


2288 


998174 


19 


963255 


2307 


036745 


45 


16 


962801 


2280 


998163 


19 


964639 


23oo 


o3536i 


44 


17 


964170 


2273 


998l5l 


19 


966019 


22o3 


033981 


43 


18 


965534 


2266 


998l3o 


20 


967394 


2286 


032606 


42 


19 


966893 


2259 


998128 


20 


968766 


2279 


o3i234 


4i 


20 


968249 


2252 


998116 


20 


97oi33 


2271 


029867 


4o 


21 


8-969600 


2244 


9-998104 


20 


8-971496 


2265 


ii"0285o4 


3 9 


22 


970947 


2238 


998092 


20 


972855 


2257 


027145 


38 


23 


972289 


223l 


998080 


20 


974209 


225l 


026791 


37 


24 


973628 


2224 


998068 


20 


97556o 


2244 


024440 


36 


25 


974962 


2217 


998056 


20 


976906 


2237 


023094 


35 


26 


976293 


2210 


998044 


20 


978248 


2230 


021702 


34 


27 


977619 


2203 


998o32 


20 


979586 


2223 


020414 


33 


20 


978941 


2197 


998020 


20 


980921 


2217 


019079 


32 


2 9 


980259 
9 8i5 7 3 


219O 


998008 


20 


982251 


2210 


017749 


3i 


3o 


2i83 


997996 


20 


983577 


2204 


016423 


3o 


3i 


8-982883 


2177 


9.997984 


20 


8-984899 


2197 


ii.oi5ioi 


29 


32 


984189 


2170 


997972 


20 


986217 


219I 


013783 


28 


33 


985491 


2i63 


997959 


20 


987532 


2l84 


012468 


27 


34 


986789 


2157 


99794] 


20 


988842 


2178 


oiii58 


26 


35 


988083 


2i5o 


997935 


21 


990149 


2171 


ooo85i 


25 


36 


989374 


2144 


997922 


21 


99i45i 


2i65 


008549 


24 


37 


990660 


2i38 


9979IO 


21 


992750 


2i58 


007260 


23 


38 


991943 


2l3l 


997897 


21 


994045 


2l52 


006955 


22 


39 


993222 


2125 


997885 


21 


995337 


2146 


004663 


21 


4o 


994497 


2119 


997872 


21 


996624 


2140 


003376 


20 


4i 


8-995768 


2112 


9-997860 


21 


8-997908 


2i34 


11-002092 


IO 


42 


997036 


2106 


997847 


21 


999188 


2127 


000812 


lb 


43 


998299 


2100 


997835 


21 


9-000465 


2121 


10-999535 


17 


44 


999560 


20o4 


997822 


21 


001738 


2Il5 


998262 


16 


45 


9-000816 


2087 


997809 


21 


003007 


2109 


996993 


i5 


46 


002069 


2082 


997797 


21 


004272 


2io3 


995728 


14 


47 


oo33i8 


2076 


997784 


21 


oo5534 


2097 


994466 


i3 


48 


oo4563 


2070 


997771 


21 


006792 


20OI 


993208 


12 


4 9 


oo58o5 


2064 


997758 


21 


008047 


2o85 


991953 


11 


5o 


007044 


2o58 


997745 


21 


009298 


2080 


990702 


10 


5i 


9-008278 


2052 


9-997732 


21 


9-010546 


2074 


10-989454 


9 


52 


009510 


2046 


997719 


21 


01 1790 


2068 


980210 


8 


53 


010737 


2040 


997706 


21 


oi3o3i 


2062 


986969 


7 


54 


01 1962 


2o34 


997693 


22 


014268 


2o56 


985732 


6 


55 


0i3i82 


2029 


997680 


22 


oi55o2 


2o5i 


984498 


5 


56 


014400 


2023 


997667 


22 


016732 


2045 


983268 


4 


57 


oi56i3 


2017 


997654 


22 


017959 


2040 


982041 


3 


58 


016824 


2012 


997641 


22 


019183 


2o33 


980817 


2 


5 9 


oi8o3i 


2006 


997628 


22 


o2o4o3 


2028 


979597 


1 


6o 


019235 


2000 


997614 


22 


021620 


2023 


978380 







Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


/ 


) 














34° 



24 


LOGARITHMIC SINES, 


TANGENTS, ETC 


Table II. 


6° 














173° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


f 





9'0I9235 


2000 


9-9976I4 


22 


9-021620 


2023 


10-978380 


60 


i 


020435 


i 9 q5 


097601 


22 


022834 


2017 


977166 


5 9 


2 


021632 


1989 


997588 


22 


024044 


2011 


97^56 


58 


3 


022825 


1984 


997574 


22 


02525l 


2006 


97474Q 


5 7 


4 


024016 


1978 


997561 


22 


026455 


2000 


973545 


56 


5 


025203 


1973 


997547 


22 


027655 


1995 


972345 


55 


6 


026386 


1967 


997534 


23 


028852 


I99O 


971 148 


54 


I 


027567 


1962 


997520 


23 


o3oo46 


1985 


969954 


53 


028744 


i 9 5 7 


997507 


23 


o3i237 


I979 


968763 


52 


9 


029918 


1951 


9974o3 


23 


o32425 


1974 


967575 


5i 


10 


031089 


1947 


997480 


23 


033609 


I969 


966391 


5o 


ii 


9-o32257 


1941 


9-997466 


23 


9-034791 


I964 


IO-965209 


4q 


12 


o3342i 


ig36 


997452 


23 


035969 


1958 


96403 1 


48 


i3 


034582 


1930 


997439 


23 


037144 


1953 


962856 


47 


14 


035741 


1925 


997425 


23 


o383i6 


1948 


961684 


46 


i5 


036896 


1920 


99741 1 


23 


039485 


1943 


96o5i5 


45 


16 


o38o48 


1915 


997397 


23 


0406 5 1 


i 9 38 


959349 


44 


12 


039197 


1910 


997383 


23 


o4i8i3 


i 9 33 


958187 


43 


o4o342 


1905 


997369 


23 


042973 


1928 


957027 


42 


19 


04U85 


1899 


997355 


23 


o44 1 3o 


1923 


955870 


4i 


20 


042625 


1894 


997341 


23 


045284 


1918 


954716 


4o 


21 


9-043762 


1889 


9.997327 


24 


9-046434 


1913 


10-953566 


39 


22 


044895 


1884 


9973 1 3 


24 


047582 


1908 


952418 


38 


23 


046026 


1879 


997299 


24 


048727 


i 9 o3 


951273 


37 


24 


047 1 54 


i8 7 5 


997285 


24 


049869 


1898 


95oi3i 


36 


25 


048279 


1870 


997271 


24 


o5ioo8 


i8 9 3 


948992 


35 


26 


049400 


1 865 


997257 


24 


o52i44 


1889 


947856 


34 


27 


o5o5io 


i860 


997242 


24 


053277 


1884 


946723 


33 


20 


o5i635 


i855 


997228 


24 


054407 


1879 


945593 


32 


29 


952749 


i85o 


997214 


24 


o55535 


1874 


944465 


3i 


3o 


o5385 9 


i845 


997199 


24 


o56659 


1870 


943341 


3o 


3i 


9-054966 


1 841 


9-997185 


24 


9-057781 


1 865 


10-942219 


29 


32 


056071 


i836 


997170 


24 


058900 


1869 


941 100 


28 


33 


057172 
058271 


i83i 


997 1 56 


24 


060016 


i855 


9 3 9 o84 


27 


34 


1827 


997141 


24 


o6u3o 


i85i 


938870 


26 


35 


059367 


1822 


997127 


24 


062240 


1846 


937760 


25 


36 


060460 


1817 


997112 


24 


o63348 


1842 


936652 


24 


37 


o6i55i 


i8i3 


997oq8 


24 


o64453 


1837 


935547 


23 


3£ 


062639 


1808 


997083 


25 


065556 


i833 


934444 


22 


3 9 


063724 


1804 


997068 


25 


o66655 


1828 


933345 


21 


4o 


064806 


1799 


997o53 


25 


067752 


1824 


932248 


20 


4i 


9-o65885 


1794 


9- 997039 


25 


9-068846 


1819 


io-93n54 


IO 


42 


066962 


1790 


997024 


25 


069938 


i8i5 


930062 


10 


43 


o68o36 


1786 


997009 


25 


071027 


1810 


928973 


iT' 


44 


069107 


1781 


996994 


25 


072113 


1806 


927887 


16 


45 


070176 


1777 


996979 


25 


073197 


1802 


926803 


i5 


46 


071242 


1772 


996964 


25 


074278 


1797 


925722 


14 


47 


072306 


1768 


996949 


25 


075356 


i 7 q3 


924644 


i3 


48 


073366 


1763 


996934 


25 


076432 


1789 


9 23568 


12 


P 


074424 


i 7 5o 


996919 


25 


077505 


1784 


922495 


11 


5o 


075480 


i 7 55 


996904 


25 


078576 


1780 


921424 


10 


5i 


9-076533 


1750 


9-996889 


25 


9-079644 


1776 


10-920356 





52 


077583 


1746 


996874 


25 


080710 


1772 


919290 


8 


53 


078631 


1742 


996858 


25 


081773 


1767 


918227 


7 


54 


079676 


1738 


996843 


25 


o82833 


1763 


917167 


6 


55 


080719 


1733 


996828 


25 


083891 


1759 


916109 


5 


56 


081759 


1729 


996812 


26 


084947 


1755 


9i5o53 


4 


5 7 


082797 


1725 


996797 


26 


086000 


i 7 5i 


914000 


3 


58 


o83832 


1721 


996782 


26 


087050 


1747 


912950 


2 


5 9 


084864 


1717 


996766 


26 


088098 


1743 


911902 


1 


60 


085894 


i 7 i3 


996751 


26 


089144 


1738 


9io856 





/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


1 


96 c 


> 












83° 



Table II. LOGARITHMIC SINES 


, TANGENTS, ETC. 25 


7° 














172° 


i 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


t 


o 


9-080894 


I7l3 


9-996751 


26 


9-089144 


1738 


10-910856 


60 


i 


086922 


1709 


996735 


26 


090187 


1734 


909813 


5 9 


2 


087947 


1704 


996720 


26 


091228 


l73o 


908772 


58 


3 


088970 


1700 


996704 


26 


092266 


1727 


907734 


57 


4 


089990 


1696 


996688 


26 


093302 


1722 


906698 


56 


5 


091008 


1692 


996673 


26 


094336 


1719 


906664 


55 


6 


092024 


1688 


99 665 7 


26 


095367 


I 7 I3 


904633 


54 


7 


093037 


1684 


996641 


26 


096395 


I7II 


9o36o5 


53 


8 


094047 


1680 


996625 


26 


097422 


1707 


902578 


32 


9 


096056 


1676 


996610 


26 


098446 


1703 


90i554 


5i 


10 


096062 


l6 7 3 


996594 


26 


099468 


1699 


900532 


5o 


II 


9-097065 


1668 


9-996578 


27 


9.100487 


i6 9 5 


10-899513 


49 


12 


098066 


i665 


996562 


27 


ioi5o4 


1691 


898496 


48 


i3 


099065 


1661 


996546 


27 


102519 


1687 


897481 


47 


14 


100062 


1657 


99653o 


27 


io3532 


1684 


896468 


46 


i5 


ioio56 


i653 


996514 


27 


104542 


1680 


8 9 5458 


45 


16 


102048 


1649 
1643 


996498 


27 


io555o 


1676 


894450 


44 


17 


io3o37 


996482 


27 


io6556 


1672 


893444 


43 


18 


I0402D 


1641 


996465 


27 


107559 


1669 


892441 


42 


19 


io5oio 


i638 


996449 


27 


io856o 


i665 


891440 


41 


20 


105992 


i634 


996433 


27 


109559 


1661 


890441 


4o 


21 


9-106973 


i63o 


9-9964I7 


27 


g.II0556 


i658 


10-889444 


3 9 


22 


107961 


1627 


996400 


27 


1 1 i55i 


1 654 


888449 


38 


23 


108927 


1623 


99 6384 


27 


1 1 2543 


i65o 


887457 


37 


24 


1 0990 1 


1619 


99 6368 


27 


n3533 


1 646 


886467 


36 


25 


1 10873 


1616 


996351 


27 


U452I 


i643 


885479 


35 


26 


1 1 1842 


1612 


996335 


27 


n55o7 


i63 9 


884493 


34 


27 


1 1 2809 


1608 


996318 


27 


116491 


i636 


8835o 9 


33 


28 


1 13774 


i6o5 


996302 


28 


1 17472 


1632 


882528 


32 


29 


1 14737 


1601 


996285 


28 


1 1 8452 


1629 


881648 


3i 


3o 


1 1 56 9 8 


1 5 97 


996269 


28 


1 1 9429 


i625 


880571 


3o 


3i 


9-n6656 


1 594 


9-996252 


28 


9.120404 


1622 


10-879596 


20 


32 


117613 


1590 


996235 


28 


121377 


1618 


878623 


28 


33 


1 18567 


i5§ 7 


996219 


28 


122348 


i6i5 


877652 


27 


34 


119619 


1 583 


996202 


28 


123317 


1611 


876683 


26 


35 


120469 


i58o 


996185 


28 


124284 


1607 


875716 


25 


36 


121417 


i5 7 6 


996168 


28 


126249 


1604 


874751 


24 


37 


122362 


i5 7 3 


996151 


28 


126211 


1601 


873789 


23 


38 


I233o6 


1569 


996134 


28 


127172 


1 597 


872828 


22 


3 9 


124248 


1 566 


9961 17 


28 


i28i3o 


1594 


871870 


21 


4o 


125187 


l562 


996100 


28 


129087 


1691 


870913 


20 


4i 


9-126125 


i559 


9-996083 


29 


9-i3oo4i 


1587 


10-869959 


JO 


42 


127060 


1 556 


996066 


29 


1 30994 


1 584 


869006 


10 


43 


127993 


i552 


996049 


29 


131944 


i58i 


868o56 


17 


44 


128925 


i54§ 


996032 


29 


i328 9 3 


1 577 


867107 


16 


45 


129854 


1 543 


996015 


29 


i33839 


1 574 


866161 


i5 


46 


130781 


1 542 


995998 


29 


134784 


1 57 1 


8652i6 


14 


47 


131706 


1539 


996980 


29 


i35 7 26 


1 56 7 


864274 


i3 


48 


i3263o 


i535 


996963 


29 


136667 


1 564 


863333 


12 


49 


i3355i 


i532 


993946 


29 


137605 


i56i 


862395 


11 


5o 


134470. 


1529 


996928 


29 


138542 


i558 


86i458 


10 


5i 


9-i35387 


i525 


9-995911 


29 


9-139476 


i555 


io-86o524 


Q 


52 


i363o3 


l522 


995894 


29 


140409 


i55i 


85 9 59i 


8 


53 


137216 


1519 


995876 


29 


i4i34o 


1 548 


85866o 


7 


54 


i38i28 


i5i6 


995859 


29 


142269 


1 545 


857731 


6 


55 


139037 


l5l2 


995841 


29 


143196 


1 542 


8568o4 


5 


56 


139944 


1 509 


995823 


29 


144121 


1 53 9 
i535 


855879 


4 


5 7 


140860 


i5o6 


995806 


29 


i45o44 


854956 


3 


58 


I4I754 


i5o3 


995788 


29 


145966 


i532 


854o34 


2 


5 9 


U2655 


i5oo 


996771 


29 


146885 


1529 


853u5 


1 


60 


U3555 


U96 


995753 


29 


147803 


i526 


852197 





/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


/ 


97° 














82° 



26 


LOGARITHMIC SINES, 


TANGENTS, ETC 


Table II. ! 


8 o 














171° j 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


/ 





9.143555 


1496 


9-995753 


3o 


9-147803 


1 526 


10-852197 


60 


i 


144453 


1493 


996735 


3o 


U8718 


i523 


85i282 


5o 


2 


U5349 


I4Q0 


996717 


3o 


149632 


1 520 


85o368 


58 


3 


146243 


1487 


995699 


3o 


i5o544 


i5i 7 


849466 


57 


4 


I47I36 


1484 


995681 


3o 


i5i454 


i5i4 


848546 


56 


5 


148026 


1481 


995664 


3o 


152363 


i5ii 


847637 


55 ! 


6 


1489 1 5 


U78 


995646 


3o 


153269 


i5o8 


846731 


54 


I 


149802 


1475 


993628 


3o 


i54i74 


i5o5 


846826 


53 ; 


i5o686 


U72 


995610 


3o 


1 55077 


l5o2 


844923 


52 


9 


i5i569 


U69 


995591 


3o 


155978 


1499 


844022 


5i ; 


10 


i5245i 


1466 


995573 


3o 


1 56877 


1496 


843i23 


5o | 


ii 


9'i5333o 


1463 


9-995555 


3o 


9.167775 


1493 


10-842225 


49 


12 


154208 


1460 


995537 


3o 


1 586 7 i 


1490 


841329 


48 


i3 


i55o83 


1457 


995519 


3o 


i5 9 565 


1487 


840435 


47 


U 


i55 9 5 7 


1454 


9955oi 


3i 


160457 


1484 


83 9 543 


46 


i5 


1 5683o 


i45i 


995482 


3i 


i6i347 


148 1 


838653 


45 


16 


157700 


1448 


995464 


3i 


162236 


1479 


837764 


44 


17 


i5856 9 


1445 


995446 


3i 


i63i23 


1476 


836877 


43 


18 


i5g435 


1442 


995427 


3i 


164008 


1473 


835992 


42 


19 


i6o3oi 


1439 


995409 


3i 


164892 


1470 


835io8 


4i 


20 


161 164 


1436 


995390 


3i 


i65 77 4 


1467 


834226 


4b 


21 


9-162025 


1433 


9-995372 


3 1 


9.166654 


1464 


10-833346 


39 


22 


162885 


i43o 


995353 


3i 


i6 7 532 


1461 


832468 


38 


23 


163743 


1427 


995334 


3i 


168409 


1458 


83 1 691 


n 


24 


164600 


1424 


9953i6 


3i 


169284 


1455 


830716 


25 


165454 


1422 


995297 


3i 


170157 


1453 


829843 


35 


26 


166307 


1419 


995278 


3i 


171029 


i45o 


828971 


34 


[2 


167159 


1416 


995260 


3i 


17 1 899 


1447 


828101 


33 


168008 


Ui3 


995241 


32 


172767 


1444 


827233 


32 


29 


168856 


1410 


995222 


32 


173634 


1442 


826366 


3i 


3o 


169702 


1407 


9952o3 


32 


174499 


i43 9 


8255oi 


3o 


3i 


9-170547 


i4o5 


9-995184 


32 


9.175362 


1436 


10-824638 


3 


32 


171389 


1402 


996165 


32 


176224 


1433 


823776 


33 


172230 


l3 99 


995146 


32 


i77 o8 4 


143 1 


822916 


27 


34 


173070 


1 3 9 6 


995127 


32 


177942 


1428 


822058 


26 


35 


173908 


i3 9 4 


995108 


32 


178799 
179655 


U25 


821201 


25 


36 


174744 


i3qi 


995089 


32 


1423 


820345 


24 


37 


175578 


i388 


995070 


32 


i8o5o8 


1420 


819492 


23 


38 


176411 


i386 


995o5i 


32 


i8i36o 


1417 


818640 


22 


3 9 


177242 


1 383 


995o32 


32 


182211 


i4i5 


817789 


21 


40 


178072 


i38o 


995oi3 


32 


i83o5 9 


1412 


816941 


20 


41 


9-178900 


1377 


9-994993 


32 


9.183907 


1409 


10-816093 


IO 


42 


179726 


i374 


994974 


32 


184752 


1407 


815248 


l8 


43 


i8o55i 


1372 


994955 


32 


186697 


1404 


814403 


17 


44 


181374 


i36 9 


994935 


32 


186439 


1402 


8i356i 


16 


45 


182196 


1 366 


994916 


33 


187280 


l3 99 


812720 


i5 


46 


i83oi6 


1 364 


994896 


33 


188120 


1 3 9 6 


811880 


14 


47 


183834 


i36i 


994877 


33 


i88 9 58 


i3q3 


811042 


i3 


48 


1 8465 1 


i35o 


994857 


33 


189794 


i3 9 i 


810206 


12 


49 


185466 


i356 


994838 


33 


190629 


i3§ 9 


809371 


11 


5o 


186280 


i353 


994818 


33 


191462 


i386 


8o8538 


10 


5i 


9-187092 


i35i 


9.994798 


33 


9-192294 


i384 


10-807706 





52 


187903 


1 348 


994779 


33 


193124 


i38i 


806876 


8 


53 


188712 


1 346 


994759 


33 


193953 


1379 


806047 


7 


54 


i8 9 5io 


i343 


994739 


33 


194780 


1376 


8o5220 


6 


55 


190323 


i34i 


994720 


33 


196606 


1374 


804394 


5 


56 


191130 


i338 


994700 


33 


196430 


i3 7 i 


803570 


4 


ll 


191933 


1 336 


994680 


33 


197253 


i36 9 


802747 


3 


192734 


i333 


994660 


33 


198074 


1 366 


801926 


2 


5 9 


193534 


i33o 


994640 


33 


198894 


1 364 


801 106 


1 


60 


194332 


i328 


994620 


33 


199713 


i36i 


800287 



/ 


/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


'98 c 


i 












81° | 



Table II. LOGARITHMIC SINES 


, TANGENTS, ETC. 


27 


9° 














170° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


t 





9'194332 


i3 2 8 


9-994620 


33 


9-199713 


i36i 


10-800287 


60 


i 


I95129 


i326 


994600 


33 


200529 


i35 9 


799471 


59 


2 


195925 


1323 


994080 


33 


20l345 


i356 


798655 


58 


3 


I96719 


l32I 


» 994560 


34 


202 1 59 


i354 


797841 


57 


4 


I975u 


i3i8 


994540 


34 


202971 


1352 


797029 


56 


5 


I98302 


i3i6 


994519 


34 


203782 


1 349 


796218 


55 


6 


I 9909 I 


i3i3 


994499 


34 


204692 


i347 


795408 


54 


7 


199879 


i3ii 


994479 


34 


2o5400 


1 345 


794600 


53 


8 


200666 


i3o8 


99445q 


34 


206207 


i342 


793793 


52 


9 


2oi45i 


i3o6 


994438 


34 


207013 


i34o 


792987 


5i 


10 


202234 


i3o4 


994418 


34 


207817 


i338 


792183 


5o 


n 


9-2o3oi7 


i3oi 


9-994398 


34 


9-208619 


1335 


10-791381 


4q 


12 


203797 


1299 


994377 


34 


209420 


1333 • 


790580 


48 


i3 


204577 


1296 


994357 


34 


210220 


i33i 


789780 


47 


i4 


2o5354 


1294 


994336 


34 


2IIOl8 


i328 


788982 


46 


i5 


2o6i3i 


1292 


9943i6 


34 


2Il8l5 


1326 


788185 


45 


16 


206906 


1289 


994295 


34 


2I26lI 


i324 


787389 


44 


n 


207679 


1287 


994274 


35 


2i34o5 


l32I 


7865 9 5 


43 


18 


208452 


1285 


994254 


35 


214198 


i3io 


785802 


42 


19 


209222 


1282 


994233 


35 


214989 


i3i 7 


785ou 


4i 


20 


209992 


1280 


994212 


35 


215780 


i3i5 


784220 


4o 


21 


9-210760 


1278 


9-994191 


35 


9-2i6568 


l3l2 


10-783432 


3 9 


22 


211626 


1275 


994171 


35 


217356 


i3io 


782644 


38 


23 


212291 


1273 


994 1 5o 


35 


218142 


i3o8 


781858 


37 


24 


2i3o55 


1271 


994129 


35 


218926 


i3o5 


781074 


36 


25 


2i38i8 


1268 


994100 


35 


219710 


i3o3 


780290 


35 


26 


214579 


1266 


994087 


35 


220492 


i3oi 


77o5o8 


34 


2 


2i5338 


1264 


994066 


35 


221272 


1299 


778728 


33 


216097 


1261 


994045 


35 


222062 


1297 


777948 


32 


2 9 


2i6854 


1259 


994024 


35 


222830 


1294 


777170 


3i 


3o 


217609 


1257 


994oo3 


35 


223607 


1292 


776393 


3o 


3i 


9-2i8363 


1255 


9-993982 


35 


9-224382 


1290 


10-775618 


29 


32 


219116 


1253 


993960 


35 


226l56 


1288 


774844 


28 


33 


219868 


1250 


993939 


35 


225929 


1286 


774071 


27 


34 


220618 


1248 


99 3oi8 


35 


226700 


1284 


7733oo 


26 


35 


221367 


1246 


993897 


36 


227471 


1281 


772529 


25 


36 


222Il5 


1244 


993875 


36 


228239 


1279 


771761 


24 


3? 


22286l 


1242 


99 3854 


36 


229OO7 


1277 


770993 


23 


38 


2236o6 


1239 


993832 


36 


229773 


1275 


770227 


22 


3 9 


224349 


1237 


99381 1 


36 


23o539 


1273 


769461 


21 


4o 


225092 


1235 


993789 


36 


23l302 


1271 


768698 


20 


4i 


9-225833 


1233 


9-993768 


36 


9-232o65 


1269 


10-767935 


IO 


42 


226573 


I23l 


993746 


36 


232826 


1267 


767174 


l8 


43 


227311 


1228 


993725 


36 


233586 


1265 


766414 


17 


44 


228048 


1226 


993703 


36 


234345 


1262 


765655 


16 


45 


228784 


1224 


993681 


36 


235io3 


1260 


764897 


i5 


46 


229618 


1222 


993660 


36 


23585g 


1258 


764141 


14 


47 


230252 


1220 


9 9 3638 


36 


2366i4 


1256 


763386 


i3 


48 


230984 


1218 


993616 


36 


237368 


1254 


762632 


12 


49 


23l7l5 


1216 


993594 


37 


238120 


1252 


761880 


11 


5o 


232444 


1214 


993572 


37 


238872 


1250 


761128 


10 


5i 


9-233172 


1212 


9-99355o 


37 


9-239622 


1248 


10-760378 





52 


233899 


1209 


993528 


37 


240371 


1246 


759629 


8 


53 


234626 


1207 


9935o6 


37 


241118 


1244 


758882 


7 


54 


235340 


1206 


993484 


37 


241865 


1242 


7 58i35 


6 


55 


236073 


1203 


993462 


37 


242610 


1240 


757390 


5 


56 


236795 


1201 


993440 


37 


243354 


1238 


756646 


4 


57 


237615 


1 199 


993418 


37 


244097 


1236 


755903 


3 


58 


238235 


1197 


993396 


37 


244839 


1234 


755i6i 


2 


5 9 


238 9 53 


1 195 


993374 


37 


245579 


1232 


754421 


1 


60 


239670 


1193 


99335i 


37 


246319 


1230 


75368i 





/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


99 c 














1 


;o° 



28 


LOGARITHMIC SINES, 


TANGENTS, ETC. Table II. 


10 c 














169° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


1 





9*239670 


1 1 9 3 


9-99335i 


37 


9-246319 


1230 


IO-75368l 


60 


i 


240386 


II91 


993329 


37 


247057 


1228 


752943 


5 9 


2 


241 101 


H89 


993307 


37 


247794 


1226 


752206 


58 


3 


241814 


1 187 


993284 


37 


24853o , 


1224 


751470 


5 7 


4 


242526 


u85 


993262 


37 


249264 


1222 


75o736 


56 


5 


243237 


u83 


993240 


37 


249998 


1220 


750002 


55 


6 


243947 


1181 


993217 


38 


25o73o 


I2l8 


740270 


54 


7 


244656 


1179 


993195 


38 


25i46i 


1217 


748539 


53 


8 


245363 


1177 


993172 


38 


252191 


12l5 


747809 


52 


9 


246069 


n 7 5 


993149 


38 


252920 


1213 


747080 


5i 


10 


246775 


n 7 3 


993127 


38 


253648 


I2II 


746352 


5o 


ii 


9-247478 


1171 


9-993104 


38 


9-254374 


1209 


10-745626 


4o 


12 


248181 


1169 


993081 


38 


255ioo 


1207 


744900 


48 


i3 


248883 


1 167 


993059 


38 


255824 


1205 


744H 6 


47 


i4 


249583 


n65 


993o36 


38 


256547 


1203 


743453 


46 


i5 


250282 


Ii63 


9930 1 3 


38 


257269 


1201 


742731 


45 


16 


250980 


1161 


992990 


38 


257990 


1200 


742010 


44 


*7 


251677 


n5 9 


992967 


38 


258710 


II98 


741290 


43 


18 


252373 


n58 


992944 


38 


259429 


1 196 


740571 


42 


19 


253067 


n56 


992921 


38 


260146 


1 1 9 4 


739854 


4i 


20 


253761 


n54 


992898 


38 


26o863 


II92 


73 9 i3 7 


4o 


21 


9-254453 


Il52 


9-992875 


38 


9-261578 


I IOO 


10-738422 


39 


22 


255i44 


u5o 


992852 


38 


262292 


H89 


737708 


38 


23 


255834 


1 148 


992829 


3 9 


263oo5 


1 187 


736995 


37 


24 


256523 


1 146 


992806 


3 9 


263717 


n85 


736283 


36 


25 


257211 


1 144 


992783 


3 9 


264428 


n83 


735572 


35 


26 


257898 


1142 


992759 


3 9 


265i38 


1181 


734862 


34 


27 


258583 


1141 


992736 


3 9 


265847 


1170 


734i53 


33 


28 


259268 


n3 9 


992713 


3 9 


266555 


1178 


733445 


32 


29 


259951 


n3 7 


992690 


3 9 


267261 


1176 


732739 


3i 


3o 


26o633 


u35 


992666 


3 9 


267967 


1174 


732o33 


3o 


3i 


9-26i3i4 


u33 


9-992643 


3 9 


9-268671 


1172 


io-73i32o 


29 


32 


261994 


ii3i 


992619 


3 9 


269375 


IT 

1169 


73o62D 


28 


33 


265673 


n3o 


992596 


?9 


270077 


729923 


27 


34 


26335i 


1128 


992572 


39 


270779 


1 167 


729221 


26 


35 


264027 


1126 


992549 


39 


271479 


n65 


728521 


25 


36 


264703 


1124 


992525 


39 


272178 


1 164 


727822 


24 


37 


265377 


1122 


9925oi 


3 9 


272876 


1162 


727124 


23 


38 


266o5i 


1120 


992478 


4o 


273573 


1 160 


726427 


22 


3 9 


266723 


1119 


992454 


4o 


274269 


u58 


725731 


21 


40 


267395 


1117 


992430 


4o 


274964 


n5 7 


725o36 


20 


4i 


9 -268o65 


iu5 


9-992406 


4o 


9-275658 


n55 


10-724342 


IO 


42 


268734 


in3 


992382 


4o 


276351 


u53 


723649 


18 


43 


269402 


mi 


99235a 


4o 


277043 


ii5i 


722957 


H 


44 


270069 


mo 


992335 


40 


277734 


n5o 


722266 


16 


45 


270736 


1108 


9923n 


40 


278424 


1 148 


721576 


i5 


46 


271400 


1 106 


992287 


4o 


279113 


1 147 


720887 


14 


47 


272064 


no5 


992263 


4o 


279801 


1 145 


720199 


i3 


48 


272726 


no3 


992239 


40 


280488 


1 U3 


7io5i2 


12 


i 9 


273388 


IIOI 


992214 


40 


281174 


ii4i 


718826 


11 


5o 


274049 


1099 


992190 


40 


28i858 


1140 


718142 


10 


5i 


9-274708 


1098 


9-992166 


4o 


9-282542 


n38 


10-717458 


9 


52 


275367 


1096 


992142 


40 


283225 


n36 


716775 


8 


53 


276026 


1094 


992118 


4i 


283907 


n35 


716093 


7 


54 


276681 


1092 


992093 


41 


284088 


n33 


715412 


6 


55 


277337 


1091 


992069 


41 


285268 


n3i 


7U732 


5 


56 

5 7 


277991 


1089 


992044 


41 


285947 


n3o 


7i4o53 


4 


278645 


1087 


992020 


41 


286624 


1128 


713376 


3 


58 


279297 


1086 


991996 


41 


287301 


1126 


712699 


2 


5 9 


279948 


1084 


991971 


41 


287977 


1125 


712023 


1 


60 


280699 


1082 


991947 


41 


288652 


1123 


711348 





1 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


i 


10( 


)° 












79° 



Table II LOGARITHMIC SINES 


, TANGENTS, ETC. 


29 


11° 












168° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


/ 





9-280599 


1082 


9.991947 


41 


9-288652 


1123 


10-711348 


60 


i 


281248 


1081 


99I922 


4l 


289326 


1 122 


710674 


5 9 


2 


281897 


1079 


991897 


4l 


289999 


1 1 20 


710001 


58 


3 


282544 


1077 


991873 


4i 


290671 


IIl8 


709329 


57 


4 


283190 


1076 


99 1 848 


4i 


291342 


III7 


708658 


56 


5 


283836 


1074 


991823 


4i 


292013 


IIl5 


707987 


55 


6 


284480 


1072 


991799 


4i 


292682 


III4 


707318 


54 


7 


285i24 


1071 


99 J 774 


42 


29335o 


I 1 12 


7o665o 


53 


8 


285766 


1069 


99 1 749 


42 


294017 


1 1 II 


705983 


52 


9 


286408 


1067 


991724 


42 


294684 


I IO9 


7o53i6 


5i 


10 


287048 


1066 


991699 


42 


295349 


I IO7 


70465 1 


5o 


ii 


9-287688 


1064 


9-991674 


42 


9-296013 


1 106 


10-703987 


4o 


12 


288326 


io63 


99 1 649 


42 


296677 


II04 


7o3323 


48 


i3 


288964 


1061 


991624 


42 


297339 


no3 


702661 


47 


1 4 


289600 


1059 


99i5 99 


42 


298001 


IIOI 


701999 


46 


i5 


290236 


io58 


991574 


42 


298662 


1 100 


70i338 


45 


16 


290870 


io56 


991549 


42 


299322 


1098 


700678 


44 


n 


291504 


io54 


991524 


42 


299980 


1096 


700020 


43 


1 8 


292137 


io53 


99 1 498 


42 


3oo638 


1095 


699362 


42 


19 


292768 


io5i 


991473 


42 


301295 


1093 


698705 


4i 


20 


293399 


io5o 


991448 


42 


301961 


1092 


698049 


4o 


21 


9-294029 


1048 


9-991422 


42 


9.302607 


1090 


10-697393 


3 9 


22 


294658 


1046 


991397 


42 


3o326i 


1089 


696739 


38 


23 


295286 


io45 


991372 


43 


303914 


1087 


696086 


37 


24 


290913 


1043 


991346 


43 


304567 


1086 


695433 


36 


25 


296039 


1042 


991321 


43 


3o52i8 


1084 


694782 


35 


26 


297164 


1040 


991295 


43 


3o586 9 


io83 


6941 3 1 


34 


27 


297788 


1039 


991270 


43 


3o65io 


1081 


693481 


33 


28 


298412 


1037 


991244 


43 


307160 


1080 


692832 


32 


29 


299034 


io36 


991218 


43 


307816 
3o8463 


1078 


692184 


3i 


3o 


299655 


io34 


991 193 


43 


1077 


691537 


3o 


3i 


9-300276 


1032 


9-991167 


43 


9.309109 


1075 


10-690891 


29 


32 


300895 


io3i 


991 141 


43 


309754 


1074 


690246 


28 


33 


3oi5i4 


1029 


991115 


43 


3 1 0399 


1073 


689601 


27 


34 


302132 


1028 


991090 


43 


3no42 


1071 


688 9 58 


26 


35 


302748 


1026 


991064 


43 


3n685 


1070 


6883 1 5 


25 


36 


3o3364 


1025 


99io38 


43 


312327 


1068 


687673 


24 


37 


303979 


1023 


991012 


43 


312968 


1067 


687032 


23 


38 


304390 


1022 


990986 


43 


3i36o8 


io65 


6863 9 2 


22 


3 9 


3o5207 


1020 


990960 


43 


3i4247 


1064 


685 7 53 


21 


4o 


3o58i9 


1019 


990934 


44 


3U885 


1062 


685u5 


20 


4i 


9-3o643o 


1017 


9-990908 


44 


g-3l5523 


1061 


10-684477 


1Q 


42 


307041 


1016 


990882 


44 


3i6i5q 


1060 


683841 


10 


43 


3©765o 


1014 


990855 


44 


316795 


io58 


683205 


n 


44 


308259 


ioi3 


990829 


44 


3 17430 


1037 


682570 


16 


45 


308867 


IOII 


990803 


44 


318064 


io55 


68i 9 36 


i5 


46 


309474 


1010 


990777 


44 


318697 


io54 


68i3o3 


14 


47 


3ioo8o 


1008 


990750 


44 


3i933o 


io53 


680670 


i3 


48 


3io685 


1007 


990724 


44 


319961 


io5i 


68oo3o 


12 


49 


3i 1289 


ioo5 


990697 


44 


320392 


io5o 


679408 


11 


5o 


3u8 9 3 


1004 


990671 


44 


321222 


1048 


678778 


10 


5i 


9-3i2495 


ioo3 


9-990645 


44 


9-32i85i 


1047 


10-678149 


Q 


52 


313097 


1001 


990618 


44 


322479 


io45 


677521 


8 


53 


3i36 9 8 


1000 


990591 


44 


323io6 


1044 


676894 


n 


54 


314297 


998 


99o565 


44 


323733 


io43 


676267 


6 


55 


314897 


997 


99o538 


44 


324358 


1041 


675642 


5 


56 


3i5495 


996 


9905 1 1 


45 


324983 


1040 


675017 


4 


5 7 


3i6oo2 


994 


990485 


45 


325607 


1039 


674393 


3 


58 


316689 


99 3 


990458 


45 


32623i 


1037 


673769 


2 


5 9 


317284 


991 


990431 


45 


326853 


io36 


673147 


1 


60 


317879 


990 


990404 


45 


327475 


io35 


672525 





/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


/ 


101 















t 


IS 



30 


LOGARITHMIC SINES 


, TANGENTS, ETC. Table II. 


12° 












167° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


1 





9.317879 


990 


9-990404 


45 


9-327475 


io35 


10.672525 


60 


i 


3l8473 


988 


990378 


45 


328095 


io33 


671905 


5 9 


2 


319066 


987 


99o35i 


45 


328715 


1032 


671285 


58 


3 


3i 9 658 


986 


990324 


45 


329334 


io3o 


670666 


5 7 


4 


320249 


9& 


990297 


45 


329953 


1029 


670047 


56 


5 


320840 


983 


990270 


45 


33o570 


1028 


669430 


55 


6 


32i43o 


982 


990243 


45 


33ll8 7 


1026 


6688i3 


54 


I 


322019 


980 


990215 


45 


33i8o3 


1025 


668197 


53 


322607 


979 


990188 


45 


3324i8 


1024 


667582 


52 


9 


323io4 


977 


990161 


45 


333o33 


1023 


666967 


5i 


10 


323700 


976 


990134 


45 


333646 


1021 


666354 


5o 


ii 


9-324366 


975 


9-990107 


46 


9-334259 


1020 


10-665741 


4q 


12 


32495o 


973 


990079 


46 


334871 


1019 


665i2o 


48 


i3 


325534 


97 2 


990052 


46 


335482 


1017 


6645i8 


47 


14 


326117 


970 


990025 


46 


336093 


1016 


663907 


46 


i5 


326700 


969 


989997 


46 


336702 


ioi5 


6632o8 


45 


16 


327281 


96J 


989970 


46 


3373i 1 


ioi3 


662689 


44 


i7 


327862 


9gg 


989942 


46 


337919 


1012 


662081 


43 


18 


328442 


9 65 


989915 


46 


338527 


IOII 


661473 


42 


19 


329021 


964 


989887 


46 


339i33 


IOIO 


660867 


4i 


20 


329599 


962 


989860 


46 


339739 


1008 


660261 


4o 


21 


9-330176 


961 


9-989832 


46 


9.340344 


1007 


10-659656 


39 


22 


330753 


960 


989804 


46 


340948 


1006 


659052 


38 


23 


33i32o 


958 


989777 


46 


34i 552 


1004 


658448 


37 


24 


33190J 


9 ll 


989749 


47 


342i55 


ioo3 


657845 


36 


25 


332478 


956 


989721 


47 


342757 


1002 


657243 


35 


26 


333o5i 


954 


989693 


47 


343358 


1000 


656642 


34 


12 


333624 


9 53 


989665 


47 


343958 


999 


656o42 


33 


334195 


952 


989637 


47 


• 344558 


998 


655442 


32 


29 


334767 


95o 


989610 


47 


345i57 


997 


654843 


3i 


3o 


335337 


949 


989582 


47 


345755 


996 


654245 


3o 


3i 


9-335906 


948 


9-989553 


47 


9.346353 


994 


10-653647 


29 


32 


336475 


946 


989525 


47 


346949 


993 


653o5i 


28 


33 


337043 


945 


989497 


47 


347545 


992 


652455 


27 


34 


337610 


944 


989469 


47 


348141 


991 


65 1 859 


26 


35 


338176 


943 


989441 


47 


348735 


990 


65i265 


25 


36 


338742 


94i 


989413 


47 


349329 


988 


650671 


24 


u 


339307 


940 


9 8 9 385 


47 


349922 


987 


650078 


23 


339871 


9 3 9 


989356 


47 


35o5i4 


986 


649486 


22 


39 


340434 


9 3 7 


989328 


47 


35no6 


9 85 


648894 


21 


40 


340996 


936 


989300 


47 


351697 


9 83 


6483o3 


20 


41 


9-34i558 


9 35 


9-989271 


47 


9.352287 


982 


10-647713 


la 


42 


3421 19 


934 


989243 


47 


352876 


981 


647124 


l8 


43 


342679 


932 


989214 


47 


353465 


980 


646535 


l l 


44 


343239 


93 1 


989186 


47 


354o53 


979 


645947 


l6 


45 


343797 


93o 


989157 


47 


35464o 


977 


64536o 


15 


46 


344355 


929 


989128 


48 


355227 


976 


644773 


14 


4 I 


344912 


927 


989100 


48 


3558i3 


975 


644187 


i3 


48 


345469 


926 


989071 


48 


3563o8 


974 


643602 


12 


i 9 


346024 


925 


989042 


48 


356982 


973 


643oi8 


11 


5o 


346579 


924 


989014 


48 


35 7 566 


971 


642434 


10 


5i 


9-347i34 


922 


9-988985 


48 


9>358i49 


970 


io-64i85i 


p 


52 


347687 


921 


9 88 9 56 


48 


358 7 3i 


960 


641269 


8 


53 


348240 


920 


988927 


48 


3593i3 


968 


640687 


7 


54 


348792 


919 


988898 


48 


35 9 8 9 3 


967 


640107 


6 


55 


349343 


917 


988869 


48 


360474 


966 


63o526 


5 


56 


349893 


916 


988840 


48 


36io53 


9 65 


638g47 


4 


57 


35o443 


9i5 


98881 1 


49 


36i632 


963 


638368 


3 


58 


350992 


914 


988782 


49 


362210 


962 


637790 


2 


5 9 


35i54o 


9i3 


988753 


49 


362787 


961 


637213 


1 


60 


352088 


911 


988724 


49 


363364 


960 


636636 




/ 


/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


102 















77° 



Table II. LOGARITHMIC SINES 


TANGENTS, ETC. 31 


13° 














166° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


1 





9-352088 


911 


9-988724 


49 


9-363364 


960 


10-636636 


60 


i 


352635 


910 


988695 


49 


363940 


9 5 9 


636o6o 


5 9 


2 


353i8i 


909 


988666 


49 


3645i5 


9 58 


635485 


58 


3 


353726 


908 


9 88636 


49 


365090 


957 


634910 


57 


4 


354271 


907 


988607 


49 


365664 


9 55 


634336 


56 


5 


3548i5 


9o5 


988578 


49 


366237 


954 


633763 


55 


6 


355358 


904 


988548 


49 


3668io 


9 53 


633190 


54 


. 7 


355901 


903 


988519 


49 


367382 


952 


6326i8 


53 


8 


356443 


902 


988489 


49 


36 7 o53 


9 5i 


632047 


52 


9 


356o84 


901 


988460 


49 


368524 


95o 


63i476 


5i 


10 


357524 


899 


988430 


49 


369094 


949 


630906 


5o 


ii 


9- 358o64 


898 


0-988401 


49 


9-369663 


948 


io-63o337 


49 


12 


3586o3 


897 


988371 


49 


370232 


946 


629768 


48 


i3 


359141 


896 


988342 


49 


370799 


945 


629201 


47 


14 


359678 


8 9 5 


9 883 12 


5o 


371367 


944 


628633 


46 


i5 


36o2i5 


8 9 3 


988282 


5o 


371933 


943 


628067 


45 


16 


360752 


892 


988252 


5o 


372499 


942 


627501 


44 


17 


361287 


891 


988223 


5o 


373064 


941 


626936 


43 


18 


361822 


890 


988193 


5o 


373629 


940 


626371 


42 


19 


362356 


889 


988163 


5o 


374193 


9 3 9 


625807 


4i 


20 


362889 


888 


9 88i33 


5o 


374756 


9 38 


625244 


4o 


21 


9-363422 


887 


9-988103 


5o 


9-375319 


9 3 7 


10-624681 


39 


22 


363g54 


885 


988073 


5o 


37588i 


9 35 


624119 


38 


23 


364485 


884 


988043 


5o 


376442 


934 


623558 


37 


24 


365oi6 


883 


9 88oi3 


5o 


377003 


9 33 


622997 


36 


25 


365546 


882 


987983 


5o 


377563 


932 


6224J7 


35 


26 


366075 


881 


987953 


5o 


378122 


93i 


621878 


34 


27 


3666o4 


880 


987922 


5o 


378681 


93o 


621319 


33 


28 


36713 1 


879 


987892 


5o 


379239 


929 


620761 


32 


29 


367659 


877 


987862 


5o 


379797 


928 


620203 


3i 


3o 


368i85 


876 


987832 


5i 


38o354 


927 


619646 


3o 


3i 


9-368711 


875 


9-987801 


5i 


9-380910 


926 


10-619090 


29 


32 


36^236 


874 


987771 


5i 


38i466 


925 


6i8534 


28 


33 


369761 


873 


987740 


5i 


382020 


924 


617980 


2.7 


34 


370285 


872 


987710 


5i 


382575 


923 


617425 


26 


35 


370808 


871 


987679 


5i 


383i29 


922 


616871 


25 


36 


37i33o 


870 


987649 


5i 


383682 


921 


6i63i8 


24 


37 


371852 


869 


987618 


5i 


384234 


920 


615766 


23 


38 


372373 


867 


987588 


5i 


384786 


919 


6i52i4 


22 


3 9 


372894 


866 


987557 


5i 


385337 


918 


6i4663 


21 


4o 


373414 


865 


987526 


5i 


385888 


917 


614112 


20 


4i 


9-373933 


864 


9-^87496 


5i 


9-386438 


9i5 


io-6i3562 


IO 


42 


374452 


863 


987465 


5i 


386987 


914 


6i3oi3 


10 


43 


374970 


862 


987434 


5i 


387536 


9i3 


612464 


17 


44 


375487 


861 


987403 


52 


388o84 


912 


611916 


16 


45 


376003 


860 


987372 


52 


38863i 


911 


611J69 


i5 


46 


376519 


85 9 


987341 


52 


389178 


910 


610822 


14 


47 


377035 


858 


987310 


52 


389724 


909 


610276 


i3 


48 


377549 


85 7 


987279 


52 


390270 


908 


609730 


12 


49 


37806J 


856 


987248 


52 


390815 


907 


6ooi85 


11 ' 


5o 


378577 


854 


987217 


52 


391360 


906 


608640 


10 


5 1 


9-379089 


853 


9-987186 


52 


9-391903 


905 


10-608097 
607553 


: 


52 


379601 


852 


987155 


52 


392447 


904 


8 


53 


38on3 


85i 


987124 


52 


392989 


903 


60701 1 


7 


•54 


380624 


85o 


987092 


52 


39353i 


902 


606469 


6 


55 


38n34 


849 


987061 


52 


394073 


901 


605927 


5 


56 


38i643 


848 


987030 


52 


39^614 


900 


6o5386 


4 


is 


382i52 


847 


986998 


52 


396154 


899 


604846 


3 


382661 


846 


986967 


5 2 • 


395694 


898 


6o43o6 


2 


5 9 


383 1 68 


845 


986936 


52 


396233 


897 


603767 


1 


60 


383675 


844 


986904 


52 


396771 


896 


603229 





/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


1 


101 


5° 












1 


76° 



32 


LOGARITHMIC SINES 


, TANGENTS, ETC. Tabu 


sit. 


14° 












165° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


/ 





9-383675 


844 


9-986904 


52 


9.396771 


896 


10-603229 


60 


i 


384i82 


843 


986873 


53 


397309 


896 


602691 


5 9 . 


2 


384687 


842 


986841 


53 


397846 


8 9 5 


602164 


58 


3 


385i92 


841 


986809 


53 


398383 


894 


601617 


57 


4 


3856 9 7 


840 


986778 


53 


398919 


8 9 3 


601081 


56 


5 


386201 


83 9 


986746 


53 


399456 


892 


6oo545 


55 


6 


386704 


838 


9867U 


53 


399990 


891 


600010 


54 


7 


387207 


83 7 


986683 


53 


4oo524 


890 


599476 


53 


8 


387709 


836 


986651 


53 


401 o58 


889 


598942 


52 


9 


3882io 


835 


986619 


53 


4oi 591 


888 


598409 


5i 


10 


3887 1 1 


834 


986587 


53 


402124 


887 


597876 


5o 


ii 


9-389211 


833 


9-986555 


53 


q- 402656 


886 


10-597344 


49 


12 


3897 1 1 


832 


986523 


53 


403.187 


885 


5 9 68 1 3 


48 


13 


390210 


83 1 


986491 


53 


403718 


884 


596282 


47 


14 


390708 


83o 


986459 


53 


404249 


883 


595751 


46 


i5 


391206 


828 


986427 


53 


404778 


882 


595222 


45 


16 


391703 


827 


9 863 9 5 


53 


4o53o8 


881 


594692 


44 


17 


392199 


826 


9 86363 


54 


4o5836 


880 


594164 


43 


18 


392693 


825 


98633i 


54 


4o6364 


879 


5 9 3636 


42 


19 


393191 


824 


986299 


54 


406892 


878 


593108 


4i 


20 


3 9 3685 


823 


986266 


54 


407419 


877 


592581 


4o 


21 


9-394179 


822 


9-986234 


54 


9.407945 


876 


io-592o55 


3 9 


22 


39467J 


821 


986202 


54 


408471 


8 7 5 


591529 


38 


23 


395166 


820 


986169 


54 


408996 


874 


591004 


37 


24 


3 9 5658 


819 


986137 


54 


409321 


874 


590479 


36 


25 


396150 


818 


986104 


54 


4ioo45 


8 7 3 


589955 


35 


26 


396641 


817 


986072 


54 


410569 


872 


58 9 43i 


34 


S 


397132 


817 


986039 


54 


411092 


871 


588 9 o8 


33 


397621 


816 


986007 


54 


4u6i5 


870 


588385 


32 


I 9 


3981 1 1 


8i5 


985974 


54 


412137 


869 


58 7 863 


3i 


3o 


398600 


814 


985942 


54 


412658 


868 


587342 


3o 


3i 


9-399088 


8i3 


9-985909 


55 


9-4i3i79 


867 


10-586821 


29 


32 


399575 


812 


985876 


55 


413699 


866 


5863oi 


28 


33 


400062 


8n 


985843 


55 


414219 


865 


585 7 8i 


27 


34 


400549 


810 


98581 1 


55 


4U738 


864 


585262 


26 


35 


4oio3d 


809 


985778 


55 


4i5257 


864 


584743 


25 


36 


4oi52o 


808 


985745 


55 


4i5775 


863 


584225 


24 


37 


4o2oo5 


807 


985712 


55 


416293 


862 


583707 


23 


38 


402489 


806 


985679 


55 


416810 


861 


583190 


22 


39 


402972 


8o5 


985646 


55 


417326 


860 


582674 


21 


4o 


4o3455 


804 


9856i3 


55 


417842 


85 9 


582i58 


20 


4i 


9-403938 


8o3 


9-98558o 


55 


9 -4i8358 


858 


io-58i642 


IO 


42 


404420 


802 


985547 


55 


418873 


85 7 


581127 


18 


43 


404901 


801 


9855U 


55 


419387 


856 


58o6i3 


17 


44 


4o5382 


800 


985480 


55 


419901 


855 


580099 


16 


45 


4o5862 


799 


985447 


55 


42041 5 


855 


579583 


i5 


46 


4o634i 


798 


985414 


56 


420927 


854 


579073 


14 


47 


406820 


797 


985381 


56 


421440 


853 


578560 


i3 


48 


407299 


796 


985347 


56 


421932 


852 


578048 


12 


,4 9 


407777 


7 9 5 


9853i4 


56 


422463 


85i 


577537 


11 


; DO 


408254 


794 


985280 


56 


422974 


85o 


577026 


10 


5i 


9-408731 


794 


9*985247 


56 


9-423484 


849 


10-576516 




52 


409207 


793 


9852i3 


56 


423993 


848 


576007 


8 j 


53 


409682 


792 


985i8o 


56 


4245o3 


848 


575497 


7 


54 


410157 


791 


985146 


56 


425oii 


847 


574989 


6 


55 


4io632 


790 


985u3 


56 


4255i9 


846 


574481 


5 1 


56 


41 1 106 


789 


985079 


56 


426027 


845 


573973 


4 j 


5 7 


41 1 579 


788 


985o45 


56 


426534 


844 


573466 


3 i 


58 


412052 


787 


985oi 1 


56 


427041 


843 


572959 


2 j 


59 


412524 


786 


984978 


56 


427547 


843 


572453 


I 


6o 


412996 


785 


984944 


56 


428o52 


842 


571948 


! 


/ 


Cosine. 


D. 


Sine. 1 


IK 


Cotang. 


D. 


Tang. 


— 1 


104 


D 












75° , 



Table II. LOGARITHMIC SINES 


, TANGENTS, ETC. 


33 


15 c 


» 












164° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


/ 





9-412996 


7 85 


9 • 984944 


^ 


9 -428o52 


842 


10-571948 


60 


i 


4l3467 


784 


984910 


57 


428558 


84l 


571442 


5 9 


2 


4i3 9 38 


783 


984876 


£1 


420062 


840 


570938 


58 


3 


4i44o8 


783 


984842 


57 


42 9 566 


83 9 


570434 


5 7 


4 


414878 


782 


984808 


57 


430070 


838 


569930 


56 


5 


4i5347 


781 


984774 


ii 


43o573 


838 


569427 


55 


6 


4i58i5 


780 


984740 


5 7 


431075 


83 7 


568 9 25 


54 


7 


416283 


779 


984706 


5 7 


43 1 577 


836 


568423 


53 


8 


416751 


778 


984672 


5 7 


43207 9 


835 


567921 


52 


9 


417217 


777 


9 84638 


57 


43258o 


834 


567420 


5i 


10 


417684 


776 


984603 


5 7 


433o8o 


833 


566920 


5o 


ii 


9-4i8i5o 


77 5 


9 • 984569 


57 


9 - 43358o 


832 


io-56642o 


4q 


12 


4i86i5 


774 


984535 


57 


434o8o 


832 


565920 


48 


i3 


419079 


773 


984500 


57 


43457 9 


83 1 


565421 


47 


14 


419544 


7 7 3 


984466 


57 


435078 


83o 


564922 


46 


i5 


420007 


772 


984432 


58 


435576 


82 9 


564424 


45 


16 


420470 


771 


984397 


58 


436073 


828 


563927 


44 


17 


420933 


770 


9 84363 


58 


436570 


828 


56343o 


43 


18 


421395 


769 


984328 


58 


437067 


827 


562933 


42 


19 


421857 


7 6§ 


984294 


58 


437563 


826 


562437 


4i 


20 


4223i8 


767 


984259 


58 


438o5 9 


825 


561941 


4o 


21 


9.422778 


767 


9-984224 


58 


9 -438554 


824 


io-56i446 


39 


22 


423238 


766 


984190 


58 


43 9 o48 


823 


560952 


38 


23 


423697 


765 


984i55 


58 


43 9 543 


823 


560457 


37 


24 


424i56 


764 


984120 


58 


44oo36 


822 


559964 


36 


25 


4246i5 


763 


9 84o85 


58 


44o52 9 


821 


559471 


35 


26 


426073 


762 


984050 


58 


441022 


820 


558978 


34 


27 


42553o 


761 


984016 


58 


44i5i4 


8i 9 


558486 


33 


28 


425987 


760 


9 83 9 8i 


58 


442006 


810 


557994 


32 


29 


426443 


760 


983946 


58 


442497 


818 


557603 


3i 


3o 


426899 


7 5 9 


98391 1 


58 


442988 


817 


557012 


3o 


3i 


9-427354 


758 


9- 9 838 7 5 


58 


9-443479 


816 


io-55652i 


29 


32 


427800 


7 5 7 


9 8384o 


5 9 


443968 


816 


556o32 


28 


33 


42826J 


756 


9 838o5 


5 9 


444458 


8i5 


555542 


27 


34 


428717 


755 


983770 


5 9 


444947 


814 


555o53 


26 


35 


429170 


754 


983735 


5 9 


445435 


8i3 


554565 


25 


36 


429623 


753 


983700 


5 9 


445923 


812 


554077 


24 


37 


43007D 


752 


983664 


5 9 


44641 1 


812 


553589 


23 


38 


43o527 


752 


983629 


5 9 


446898 


811 


553io2 


22 


3 9 


430978 


"pi 


9 835 9 4 


5 9 


447384 


810 


5526i6 


21 


4o 


431429 


75o 


9 83558 


5 9 


447870 


8o 9 


552i3o 


20 


4i 


9-431879 


749 


9-983523 


5 9 


9-448356 


8o 9 


io-55i644 


IO 


42 


43232Q 


740 


983487 


5 9 


448841 


808 


55n59 


18 


43 


432778 


748 


983452 


5 9 


449326 


807 


550674 


H 


44 


433226 


747 


9 834i6 


5 9 


449810 


806 


550190 


16 


45 


433675 


746 


9 8338i 


5 9 


450294 


806 


549706 


i5 


46 


434122 


745 


983345 


5 9 


450777 


8o5 


549223 


14 


47 


434569 


744 


983309 


5 9 


45i26o 


804 


548740 


i3 


48 


435oio 


744 


983273 


60 


45i743 


8o3 


548257 


12 


49 


435462 


743 


9 83238 


60 


452225 


802 


547775 


11 


5o 


435908 


742 


983202 


60 


452706 


802 


547294 


10 


5i 


9-436353 


74i 


9-983166 


60 


9-453187 


801 


io-5468i3 


9 


52 


436798 


740 


q83i3o 


60 


453668 


800 


546332 


8 


53 


437242 


740 


983094 


60 


454i48 


799 


545852 


7 


54 


437686 


73o 


9 83o58 


60 


454628 


799 


545372 


6 


55 


438129 


738 


983022 


60 


455io7 


798 


544893 


5 


56 


438572 


7 3 7 


982986 


60 


455586 


797 


5444U 


4 § 


5 7 


439014 


736 


982950 


60 


456o64 


7 9 6 


543936 


3 B 


58 


439456 


736 


982914 


60 


456542 


796 


543458 


2 1 


5 9 


439897 


735 


982878 


60 


457019 


7 9 5 


542981 


1 


60 


44o338 


734 


982842 


60 


4574 9 6 


794 


542604 





/ 

105 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


/ 















i 


74.0 



34 


LOGARITHMIC SINES 


, TANGENTS, ETC. Table II. 


16 


D 












163° 


t 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


/ 





9-44o338 


734 


9-982842 


60 


9-457496 


794 


io-5425o4 


60 


I 


440778 


733 


982805 


60 


457973 


7 9 3 


542027 


5 9 


2 


441218 


732 


982769 


61 


458449 


7 9 3 


54i55i 


58 


3 


44i658 


7 3i 


982733 


61 


458925 


792 


541075 


57 


4 


442096 


7 3i 


982696 


61 


459400 


791 


540600 


56 


5 


442535 


73o 


982660 


61 


459875 


790 


54oi25 


55 


6 


442973 


729 


982624 


61 


460349 


790 


539651 


54 


7 


4434io 


728 


982587 


6i 


460823 


789 


530177 


53 


8 


443847 


727 


98255l 


61 


461297 


788 


5387o3 


52 


9 


444284 


727 


9825l4 


61 


461770 


788 


53823o 


5i 


10 


444720 


726 


982477 


61 


462242 


787 


53 77 58 


5o 


ii 


9«445i55 


725 


9-982441 


61 


0-462715 


786 


10-537285 


49 


12 


445590 


724 


982404 


61 


' 463 1 86 


785 


5368U 


48 


i3 


446025 


723 


982367 


61 


463658 


785 


536342 


47 


14 


446459 


723 


98233l 


61 


464128 


784 


535872 


46 


i5 


446893 


722 


982294 


61 


464599 


783 


5354oi 


45 


16 


447326 


721 


982207 


61 


465069 


783 


53493i 


44 S 


17 


447759 


720 


982220 


62 


46553q 


782 


53446i 


43 j 


18 


448191 


720 


982183 


62 


466008 


781 


533992 


42 1 


*9 


448623 


719 


982146 


62 


466477 


780 


533523 


41 S 


20 


449054 


718 


982109 


62 


466945 


780 


533o55 


4o 8 


21 


9-449485 


717 


9-982072 


62 


9.467413 


779 


10-532587 


3o J 


22 


4499i5 


716 


982035 


62 


467880 


778 


532120 


38 | 


23 


45o345 


716 


981998 


62 


468347 


778 


53i653 


3 7 


24 


450775 


71D 


981961 


62 


468814 


777 


53u86 


36 j 


25 


45 1 204 


7i4 


981924 


62 


469280 


776 


530720 


35 I 


26 


45i632 


7 i3 


981886 


62 


469746 


7 7 5 


53o254 


34 I 


27 


452o6o 


7 i3 


981849 


62 


47021 1 


775 


529789 


33 J 


28 


452488 


712 


981812 


62 


470676 


774 


529J24 


32 ! 


29 


452915 


711 


981774 


62 


47 J i4i 


773 


52885 9 


3i I 


3o 


453342 


710 


981737 


62 


471605 


773 


528395 


3o j 


3i 


9-453768 


710 


9-981700 


63 


9.472069 


772 


10-527931 


29 ! 


32 


454194 


709 


981662 


63 


472532 


771 


527468 


28 j 


33 


454619 


708 


981625 


63 


472995 


771 


527005 


27 1 


M 


455o44 


707 


981587 


63 


473457 


770 


526543 


26 i 


35 


455469 


707 


981549 


63 


473919 


769 


526081 


25 j 


36 


4558 9 3 


706 


98l5l2 


63 


47438i 


760 


5256io 


24 B 


3 7 


4563 1 6 


7o5 


981474 


63 


474842 


766 


525i58 


23 j 


38 


456739 


704 


981436 


63 


4753o3 


767 


524697 


22 I 


3 9 


457162 


704 


981399 


63 


475763 


767 


524237 


21 1 


4o 


457584 


703 


98l36l 


63 


476223 


766 


523777 


20 


4i 


9- 458oo6 


702 


9-98l323 


63 


9.476683 


7 65 


io-5233i7 


in 


42 


458427 


701 


981285 


63 


477U2 


765 


522858 


10 


43 


458848 


701 


981247 


63 


477601 


764 


522399 


17 


44 


459268 


700 


981209 


63 


478059 


763 


521941 


16 


45 


459688 


690 


981171 


63 


478517 


763 


521483 


i5 


46 


460108 


69S 


98ll33 


64 


478975 


762 


521025 


14 


47 


460D27 


698 


981095 


64 


479432 


761 


520568 


i3 


48 


460946 


697 


981067 


64 


479889 


761 


520III 


12 


|9 


46i364 


696 


981019 


64 


48o345 


760 


519655 


11 


5o 


461782 


6 9 5 


980981 


64 


480801 


7 5 9 


519199 


10 


5i 


9-462199 


6 9 5 


9-980942 


64 


9-481257 


7 5 9 


10-518743 


9 


52 


462616 


694 


980904 


64 


481712 


7 5§ 


518288 


8 


53 


463o32 


6 9 3 


980866 


64 


482167 


7 5 7 


517833 


7 


54 


463448 


6 9 3 


980827 


64 


482621 


757 


517379 


6 


55 


463864 


692 


980789 


64 


483075 


756 


516925 


5 


56 


464279 


691 


980750 


64 


483529 


755 


516471 


4 


5 7 


464694 


690 


980712 


64 


483982 


755 


5i6oi8 


3 


58 


465 1 08 


690 


980673 


64 


484435 


754 


5i5565 


2 


5 9 


465522 


689 


98o635 


64 


484887 


753 


5i5u3 


1 


60 


465935 


688 


980596 


64 


48533 9 


753 


5u66i 


8 


/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


/ 


106 















73° | 



Table II. LOGARITHMIC SINES 


, TANGENTS, ET 


0. 


35 


17 c 














1 


52° 
60 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 





9'465935 


688 


9.980396 


64 


9-485339 


755 


io-5i466i 


i 


466348 


688 


98o558 


64 


485791 


752 


514209 


5 9 


2 


466761 


687 


980519 


65 


486242 


75i 


5i3758 


58 


3 


467173 


686 


980480 


65 


486693 


7 5i 


5i33o7 


57 


4 


467585 


685 


980442 


65 


487143 


75o 


5i2857 


56 


5 


467996 


685 


980403 


65 


487593 


749 


512407 


55 


6 


468407 


684 


98o364 


65 


488043 


74Q 


5uo57 


54 


7 


468817 


683 


98o325 


65 


488492 


748 


5iioo8 


53 


8 


469227 


683 


980286 


65 


488941 


747 


5no59 


52 


9 


469637 


682 


980247 


65 


489390 


747 


5io6io 


5i 


10 


470046 


681 


980208 


65 


489838 


746 


5ioi62 


5o 


ii 


9-470455 


680 


9-980169 


65 


9.490286 


746 


10.509714 


4q 


12 


470863 


680 


98oi3o 


65 


490733 


745 


509267 


48 


i3 


471271 


6 79 


980OQI 


65 


491 180 


744 


508820 


47 


i4 


471679 


678 


980002 


65 


491627 


744 


5o8373 


46 


i5 


472086 


678 


980012 


65 


492073 


743 


607927 


45 


16 


472492 


677 


979973 


65 


492519 


743 


507481 


44 


17 


472898 


676 


97 99 34 


66 


492965 


742 


507035 


43 


18 


473304 


676 


979890 


66 


493410 


74i 


506590 


42 


19 


473710 


675 


979835 


66 


493854 


74o 


5o6i46 


4i 


20 


474i i5 


674 


979816 


66 


494299 


740 


505701 


4o 
39 


21 


9.474519 


674 


9.979776 


66 


9-494743 


74o 


io-5o5257 


22 


474923 


6 7 3 


979737 


66 


495186 


739 


5o48i4 


38 


23 


475327 


672 


979697 


66 


49563o 


738 


504370 


37 


24 


475730 


672 


979638 


66 


496073 


737 


503927 


36 


25 


476133 


671 


979618 


66 


4965i 5 


737 


5o3485 


35 


26 


476536 


670 


979579 


66 


496937 


736 


5o3o43 


34 


27 


476938 


669 


979 53 9 


66 


497399 


736 


502601 


33 


28 


477340 


669 


979499 


66 


497841 


735 


5o2i5o 


32 


29 


477741 


668 


979439 


66 


498282 


734 


501718 


3i 


3o 


478142 


667 


979420 


66 


498722 


734 


501278 


3o 


3i 


9.478542 


667 


9.979380 


66 


9.499163 


733 


io-5oo837 


29 


32 


478942 


666 


979340 


66 


499603 


733 


500397 


28 


33 


479342 


665 


979300 


67 


5ooo42 


732 


499908 


27 


34 


479741 


665 


979260 


67 


5oo48i 


7 3i 


499519 


26 


35 


480140 


664 


979220 


67 


500920 


73i 


499080 


25 


36 


48o53 9 


663 


979180 


67 


5oi359 


y3o 


498641 


24 


37 


480937 


663 


979140 


67 


501797 


73o 


498203 


23 


38 


48i334 


662 


979100 


67 


5o2235 


720 


497765 


22 


3 9 


481731 


661 


979039 


67 


502672 


728 


497328 


21 j 


4o 


482128 


661 


979019 


67 


5o3io9 


728 


496891 


20 


4i 


9-482525 


660 


9.978979 


67 


9>5o3546 


727 


10-496454 


IQ 


42 


482921 


659 


97 8o3 9 


67 


503982 


727 


496018 


18 


43 


4833i6 


65 9 


978898 


67 


5o44i8 


726 


495582 


17 


44 


483712 


658 


978858 


67 


5o4854 


7 25 


493146 


16 j 


45 


484107 


657 


978817 


67 


505289 


723 


49471 1 


i5 1 


46 


4845oi 


657 


978777 


67 


305724 


724 


494276 


J 4 I 


47 


484895 


656 


978737 


67 


5o6i59 


"24 


493841 


i3 | 


48 


485209 


655 


9786.96 


68 


5o6593 


723 


493407 


12 R 


49 


485682 


655 


978655 


68 


507027 


722 


492973 


1 1 | 


5o 


486075 


654 


978615 


68 


507460 


722 


492040 


10 I 


5i 


9.486467 


653 


9.978574 


68 


9-507893 


721 


10.492107 


Q I 


52 


486860 


653 


978533 


68 


5o8326 


721 


491674 


I 


53 


487251 


652 


978493 


68 


508739 


720 


491 241 


7 1 


54 


487643 


65i 


978402 


68 


509191 


719 


490809 


6 6 


55 


488o34 


65i 


97841 1 


68 


509622 


719 


490378 


5 5 


56 


488424 


65o 


978370 


68 


5ioo54 


718 


489946 


4 I 


57 


488814 


65o 


978329 


68 


5 10485 


718 


489515 


3 i 


58 


489204 


649 


978288 


68 


510916 


717 


489084 


2 ! 


5 9 


48 9 5 9 3 


648 


978247 


68 


5ii346 


716 


488654 


1 


60 


489982 


648 


978206 . 


68 


511776 


716 


488224 





/ 

To7 




•Cosine. 


d. 


Sine. 


_ 

D. 


Cotang. 


D. 


Tang. 


1 















7 


2° 



36 


LOGARITHMIC SINES 


, TANGENTS, ETC. T^ble II. 


18° 












161° 


/ 


Sine. 


D. 


Cosine. 


B. 


Tang. 


D. 


Cotang. 


' 





9-489982 


648 


9-978206 


68 


9.511776 


716 


I0-488224 


60 


i 


490371 


648 


978165 


68 


5l22o6 


716 


487794 


5o, 


2 


490759 


647 


978124 


68 


5i2635 


7 i5 


487365 


58 


3 


491 147 


646 


978083 


69 


5i3o64 


7U 


486 9 36 


57 


4 


491535 


646 


978042 


69 


5 1 3493 


7i4 


486507 


56. 


5 


491922 


645 


978001 


69 


5i3g^i 


7 i3 


486079 


55 


6 


4923o8 


644 


977950 


69 


5i4349 


7 i3 


48565 1 


5A 


7 


492693 


644 


977918 


69 


5 1 4777 


712' 


4852^3 


53 


8 


493081 


643 


977877 


69 


5i52o4 


712- 


484796 


52 


9 


493466 


642 


977835 


69 


5i563i 


711 


484369 


5i 


10 


49385i 


642 


977794 


69 


5 1 6057 


710 


483 9 43 


5o> 


II 


9-494236 


641 


9.977752 


69 


9.516484 


710 


io-4835i6 


49 


12 


494621 


641 


97771 1 


69 


316910 


709 


483090 


48 


Ii3 


495oo5 


640 


977669 


69 


5r7335 


700 


482665 


47 


14 


495388 


63 9 


977628 


69 


517761 


708 


482239 


46 


i5 


495772 


63 9 


977586 


69 


5 18 1 86 


708 


481814 


45 


16 


496164 


638 


977544 


70 


5i86io 


707 


481390 


44 


17 


496537 


637 


9775o3 


70 


5^9034 


706 


480966 
480642 


43 


18 


496919 


637 


977461 


70 


5i9458 


706 


42 


19 


497301 


636 


977419 


70 


519882 


7o5 


4801 18 


4i 


20 


497682 


636 


977377 


70 


52o3o5 


706 


,479695 


4o 


21 


9-498064 


635 


9-977335 


70 


9.520728 


7<>4 


10-479272 


3 9 


22 


498444 


634 


977293 


70 


52ii5i 


703 


478849 


38 


23 


498825 


634 


97725i 


70 


52i573 


7»3 


478427 


37 


24 


499204 


633 


977209 


70 


521995 


7o3 


478005 


36 


25 


499584 


632 


977167 


70 


522417 


702 


477583 


35 


26 


499963 


632 


977125 


70 


522838 


702 


477162 


34 


27 


5oo342 


63 1 


977083 


70 


523259 


701 


476741 


33 


28 


500721 


63 1 


977041 


70 


52368o 


701 


476320 


32 


29 


501099 


63o 


976999 


70 


524100 


700 


47 5900 


3i 


3o 


501476 


629 


976937 


70 


524520 


699 


475480 


3o 


3i 


9-5oi854 


629 


9-976914 


70 


9.524940 


699 


10 -475o6o 


29 


32 


50223l 


628 


976872 


7i 


52535a 


696 


474641 


28 


33 


502607 


628 


97683o 


7i 


525778 


698 


474222 


27 


34 


502984 


627 


976787 


7i 


526197 


697 


4738o3 


26 


35 


5o336o 


626 


976745 


7i 


5266i5 


697 


473385 


25 


36 


5o3735 


626 


976702 


7i 


527033 


696 


472967 


24 


37 


5o4no 


623 


976660 


7i 


52745i 


696 


472549 


23 


38 


5o4485 


625 


976617 


7i 


527868 


6 9 5 


472132 


22 


3 9 


5o486o 


624 


976574 


7i 


528285 


6 9 5 


471715 


21 


4o 


5o5234 


623 


976532 


7i 


528702 


694 


471298 


20' 


4i 


9-5o56o8 


623 


9.976489 


7i 


9.529119 


6 9 3 


10.470881 


I? 


42 


5o5q8i 


622 


976446 


7i 


529535 


6 9 3 


470465 


43 


5o6354 


622 


976404 


7i 


529951 


693 


470049 


17 


44 


506727 


621 


976361 


7i 


53o366 


692 


469634 


16 


45 


507099 


620 


s 9763l8 


7i 


530781 


691 


469219 


i5 


46 


507471 


620 


976275 


71 


531196 


691 


468804 


14 


47 


507843 


619 


976232 


72 


53i6ii 


690 


468389 


i3 


48 


508214 


619 


976189 


72 


532025 


690 


467975 


12 


i 9 


5o8585 


618 


976146 


72 


532439 


689 


467561 


11 


5o 


508956 


618 


976103 


72 


532853 


689 


467147 


10 


5i 


9-509326 


617 


9.976060 


72 


9-533266 


688 


10-466734 





52 


509696 


616 


976017 


72 


533679 


688 


466321 


8 


53 


5 1 oo65 


616 


975974 


72 


534092 


687 


465908 


7 


54 


5io434 


6i5 


975930 


72 


5345o4 


687 


465496 


6 


55 


5io8o3 


6i5 


975887 


72 


534916 


686 


465o84 


5 


56 


511172 


614 


975844 


72 


535328 


686 


464672 


4 


57 


5n54o 


6i3 


9758oo 


72 


535739 


685 


464261 


3 


58 


511907 


6i3 


975757 


72 


536i5o 


685 


46385o 


2 


5 9 


512273 


612 


975714 


72 


53656i 


684 


46343o 


1 


6o 


512642 


612 


975670 


72 


536972 


684 


463028 





r 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


108 















1 


i° 1 



Ta 
79< 


BLE II. 


LOGARITHMIC 


SINES, TANGENTS, ETC. 


37 


> 












160° 


/ 


Sine. 


D. 


*Cosine. 


D. 


Tang. 


D. 


Cotang. 


/ 





9-5I2042 


612 


9 -.976670 


73 


9-536972 


684 


io-463o28 


60 


i 


5i3oo9 


611 


975627 


7 3 


537382 


683 


462618 


59 


2 


5i337D 


611 


975583 


73 


537792 


683 


462208 


58 


3 


613741 


610 


975539 


73 


538202 


682 


461798 


57 


4 


514107 


609 


975496 


73 


5386u 


682 


46i38 9 


56 


5 


514472 


6oo 


976462 


7 3 


539020 


681 


460980 


55 


6 


5U837 


608 


975408 


73 


539429 


681 


460671 


54 


7 


5.1 5202 


608 


975365 


73 


53 9 837 


680 


46oi63 


53 


8 


5i5566 


607 


975321 


73 


540245 


680 


459755 


52 


9 


5i592o 


607 


976277 


73 


54o653 


679 


45o347 


5i 


10 


516294 


6g6 


976233 


7 3 


541061 


679 


458939 


5o 


" 


>9-5i6657 


6o5 


9-976189 


73 


9- 54U68 


678 


so- 458532 


49 


12 


517020 


6o5 


975146 


7 3 


541875 


678 


458i25 


48 ; 


i3 


5i 7 38fi 


604 


976^01 


73 


542281 


677 


457719 


47 


U 


5i7745 


604 


975057 


73 


54^688 


677 


457312 


46 


i5 


518107 


6o3 


975oi3 


73 


543094 


676 


456oo6 


45' 


16 


5 1 8468 


6©3 


974969 


74 


5434Q9 


676 


4565oi 


44 


H 


518829 


602 


974926 


74 


543906 


6 7 5 


456095 


43 


18 


519190 


601 


974880 


74 


5443io 


675 


455690 


42 


19 


619551 


601 


974836 


74 


544715 


674 


455285 


4i 


20 


619911 


■600 


974792 


74 


545ii9 


674 


45438i 


4o 


21 


9-520271 


; 6oo 


9.974748 


74 


9-545524 


673 


20-454476 


3 9 


22 


52o63i 


599 


974703 


74 


546928 


673 


464072 


38 


23 


620990 


5 99 


974659 


74 


54633i 


672 


453669 


37 


24 


52 1 349 


5 9 8 


9746i4 


74 


546735 


672 


453265 


36 


25 


52 1 707 


598 


97457© 


74 


5473 38 


671 


452862 


35 


26 


622066 


597 


9745e5 


74 


547540 


671 


452460 


34 


27 


522424 


5 9 6 


97448i 


74 


547943 


670 


452067 


33 


.28 


522781 


5e6 


974436 


74 


548345 


670 


45i655 


32 


29 


5a3i38 


5 9 5 


974391 


74 


548747 


669 


45i253 


3i 


3o 


523495 


595 


974347 


75 


549149 


669 


45o85i 


3o 


3i 


9-523852 


594 


9- 9743o2 


7 5 


9-549550 


668 


10 -45o45o 


29 


32 


624208 


£94. 


974267 


75 


649961 


66S 


45oo49 
449648 


28 


33 


524564 


5 9 3 


974212 


75 


55o352 


667 


27 


34 


524920 


5 9 3 


974167 


75 


560762 


667 


449248 


26 


35 


525276 


592 


974122 


75 


55n53 


666 


448847 


26 


36 


52563o 


591 


974077 


75 


55i552 


666 


448448 


24 


37 


525984 


591 


974o32 


75 


551962 


665 


448048 


23 


38 


626339 


590 


973987 


75 


55235i 


665 


447649 


22 


3 9 


626693 


590 


973942 


75 


55275o 


665 


447260 


21 


4o 


527046 


58 9 


973897 


75 


553i49 


664 


44685 1 


20 

T 


£1 


9-627460 


58 9 


9-97385:2 


75 


9-553548 


664 


so-446452 


42 


527753 


588 


■973807 


75 


553o46 


663 


446064 


18 | 


43 


528i<r5 


588 


•973761 


75 


554344 


663 


445656 


n 


M 


528458 


58 7 


973716 


76 


664741 


66s 


445259 


16 


45 


52881.0 


687 


973671 


76 


555i3q 


662 


444861 


i5 


46 


629165 


586 


973625 


76 


555536 


661 


444464 


14 


•47 


529613 


586 


97358© 


76 


555933 


661 


444067 


i3 


48 


529864 ' 


585 


973535 


76 


55632Q 


660 


443671 


12 


4 9 


53o2i5 


535 


973489 


76 


556725 


660 


443275 


11 


5o 


53o565 


684 


973444 


76 


557121 


65 9 


442879 


10 


5 1 


9- 530916 


584 


9-973398 


76 


<9-5575i7 


65 9 


10-442483 


9 


5.2 


53 1 265 


583 


973332 


76 


567913 


65a 


442087 


8 


53 


53i6i4 


582 


973307 


76 


5583o8 


658 


441692 


7 


§4 


501963 


582 


973261 


76 


558703 


658 


441297 


6 


55 


5323ia 


58i 


973&i5 


76 


569097 


667 


44oqo3 


5 


56 


53266i 


58 1 


973169 


76 


559491 


667 


440009 


4 


5-7 


533o©9 


58® 


973124 


76 


55 9 885 


656 


440116 


3 


58 


533357 


58o 


973078 


76 


660279 


656 


439721 


2 


5a 


533704 


5 79 


973o32 


77 


560673 


^55 


439327 
438 9 34 


1 


60 


534o52 


578 


972986 


77 


56 1 066 


655 





/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D- 


Tang. 


/ 


10< 


)° 








• 




/ 


70° 



38 


LOGARITHMIC SINES, 


TANGENTS, ETC. Table 


II. 


20 c 














159° 


t 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


t 
60 





9«534o52 


5 7 8 


9-972986 


77 


9 .561066 


655 


10-438934 


i 


534399 


577 


972940 


77 


561459 


654 


438541 


5 9 


2 


534745 


5 77 


972894 


77 


56i85i 


654 


438i49 


58 


3 


535o92 


5 77 


972848 


77 


562244 


653 


437756 


5 7 


4 


535438 


576 


972802 


77 


562636 


653 


437364 


56 


5 


535 7 83 


576 


9727D5 


77 


563028 


653 


436972 


55 j 


6 


536129 


575 


972709 


77 


563419 


652 


43658i 


54 J 


7 


536474 


574 


972663 


77 


5638ii 


652 


436189 


53 1 


8 


5368i8 


574 


972617 


77 


564202 


65 1 


435798 


52 j 


9 


537163 


5 7 3 


972570 


77 


564593 


65i 


435407 


5i g 


10 


537507 


573 


972524 


77 


5649»3 


65o 


435oi7 


5o J 


ii 


9.037851 


572 


9.972478 


77 


9.565373 


65o 


10-434627 


49 J 


12 


538194 


572 


97243l 


78 


565763 


649 


434237 


48 1 


i3 


538538 


571 


972385 


78 


566 1 53 


649 


433847 


47 


i4 


53888o 


5 7 i 


972338 


78 


566542 


649 


433458 


46 


i5 


539223 


570 


972291 


78 


566932 


648 


433o68 


45 


16 


539565 


570 


97224.5 


78 


56732.0 


648 


43268o 


44 


H 


539907 


K 9 


972198 


78 


567709 
568oo8 


647 


432291 


43 


18 


540249 


56 9 


972101 


78 


647 


43 1 902 


42- 


J 9 


540590 


568 


972105 


78 


568486 


646 


43i5i4 


4i 


20 


540931 


568 


972058 


78 


5688 7 3 


646 


43 1 127 


4o 
3 9 


21 


9.541272 


56 7 


9.972011 


78 


9.569261 


645 


10-430739 


22 


54i6i3 


567 


971964 


78 


569648 


645 


43o352 


38 


23 


541953 


566 


971917 


78 


570035 


645 


429965 


37 


24 


542293 


566 


971870 


78 


570422 


644 


429678 


36 


25 


542632 


565 


971823 


78 


570809 


644 


429191 


35 


26 


542971 


565 


971776 


78 


571196 


643 


4288o5 


34 


27 


5433io 


564 


971729 


79 


5 7 i58i 


643 


428419 


33 


28 


543649 


564 


971682 


79 


571967 


642 


428033 


32 


29 


543987 


563 


97i635 


79 


572352 


642 


427648 


3i 


3o 


544325 


563 


97 i588 


79 


572738 


642 


427262 


3o 


3i 


9-544663 


562 


9-971540 


79 


9.573123 


641 


10-426877 


29 


32 


545ooo 


562 


971493 


79 


573507 


641 


426493 


28 


33 


545338 


56 1 


971446 


79 


573892 


640 


426108 


27 


34 


545674 


56 1 


971398 


79 


574276 


640 


425724 


26 


35 


54601 1 


56o 


97i35i 


79 


574660 


63 9 


42534o 


25 


36 


546347 


56o 


97i3o3 


79 


575044 


63 9 


424956 


24 


37 


546683 


K 9 


971256 


79 


575427 


63 9 


424673 


23 


38 


547019 


55 9 


971208 


79 


5 7 58io 


638 


424190 


22 


39 


547354 


558 


971161 


79 


57619,3 


638 


423807 


21 


4o 


547689 


558 


971113 


79 


576576 


637 


423424 


20 


4i 


9-548024 


55 7 


9.971066 


80 


9.576959 


637 


io-423o4i 


19 


42 


54835 9 


557 


971018 


80 


577341 


636 


422659 


18 


43 


548693 


556 


970970 


80 


577723 


636 


422277 


n 


44 


5490.27 


556 


970922 


80 


578104 


636 


421896 


16 


45 


5493.60 


555 


970874 


80 


578486 


635 


42i5i4 


i5 


46 


549693" 


555 


970827 


80 


578867 


635 


42 u 33 


14 


47 


55oo26 


554 


970779 


80 


579248 


634 


420752 


i3 


48 


55o359 


554 


970731 


80 


579629 


634 


420371 


12 


4 9 


550692 


553 


970683 


80 


580009 


634 


419991 


11 


5o 


55io24 


553 


970635 


80 


58o38 9 


633 


419611 


10 


5i 


9'55i356 


552 


9>97o586 


80 


9.580769. 


633 


10-419231 





5s 


551687 


552 


970538 


80 


581149 


632 


4i885i 


8 


53 


552oi8 


552 


970490 


80 


58i528 


632 


418472 


7 J 


54 


552349 


55i 


970442 


80 


581907 


632 


418093 


6 


55 


55268o 


55i 


970394 


80 


582286 


63 1 


4i77 14 


5 


56 


553oio 


55o 


970345 


81 


582665 


63 1 


417335 


4 Ii 


5t 


553341 


55o 


970297 


81 


583 o44 


63o 


416956 


3 * 


:58 


553670 


549 


970249 


81 


583422 


63o 


416578 


?! 


59. 


554ooo 


549 


970200 


81 


5838oo 


629 


416200 


60 


554329 


548 


970152 


81 


584177 


629 


4i5823 





! 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


' j 


11c 















1 


59° j 



















Table II. LOGARITHMIC SINES 


, TANGENTS, ETC. 39 


21° 














158° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


/ 





9- 55432Q 


548 


9.970152 


81 


9.584177 


629 


I0«4i5823 


60 1 


i 


554658 


548 


970103 


81 


584555 


629 


4i5445 


5g I 


2 


554987 


547 


970o55 


81 


584932 


628 


4i5o68 


58 I 


3 


5553i5 


547 


970006 


81 


5853o 9 


628 


414691 


5 7 


4 


555643 


546 


969957 


81 


585686 


627 


4i43 1 4 


56 J 


5 


555971 


546 


969909 


81 


586062 


627 


4i3 9 38 


55 j 


6 


556299 


545 


969860 


81 


586439 


627 


4i356i 


54 8 


7 


556626 


545 


96981 1 


81' 


5868 1 5 


626 


4i3i85 


53 1 


8 


556953 


544 


969762 


81 


587190 


626 


412810 


52 § 


9 


557280 


544 


969714 


81 


587566 


625 


412434 


5i 1 


10 


557606 


543 


969665 


81 


587941 


625 


412039 


5o 1 


ii 


9-557932 


543 


9-969616 


82 


9-5883i6 


625' 


10-411684 


49 


12 


558258 


543 


969567 
969518 


82 


5886 9 i 


624 


4n3o9 


48 


i3 


558583 


542 


82 


589066 


624 


410934 


47 


i4 


558909 


542 


969469 


82 


589440 


623 


4io56o 


46 


i5 


559234 


54l 


969420 


82 


58 9 8i4 


623 


410186 


45 


16 


559558 


541 


969370 


82 


590188 


623 


409812 


44 


17 


55 9 883 


54o 


969321 


82 


590562 


622 


409438 


43 


18 


560207 


540 


969272 


82 


590935 


622 


409065 


42 


l 9 


56o53i 


53 9 


969223 


82 


591308 


622 


408692 


4i 


20 


56o855 


53 9 


969173 


82 


5 9 i68i 


621 


408319 


4o 


21 


9-561178 


538 


9-969124 


82 


9.592054 


621 


10.407946 


3 9 


22 


56i5oi 


538 


969075 


82 


592426 


620 


407374 


38 


23 


56i824 


537 


969025 


82 


592799 


620 


407201 


37 


24 


562146 


537 


968976 


82 


5g3i7i 


619 


406829 


36 


25 


562468 


536 


968926 


83 


593542 


619 


406458 


35 


26 


562790 


536 


968877 


83 


593914 


618 


406086 


34 


2 7, 

28 


563ii2 


536 


968827 


83 


594285 


618 


405710 


33 


563433 


535 


968777 


83 


594656 


618 


4o5344 


32 


29 


563755 


535 


968728 


83 


595027 


617 


404973 


3i 


3o 


564075 


534 


968678 


83 


5 9 53 9 8 


617 


404602 


3o 


3i 


9-564396 


534 


9.968628 


83 


9.595768 


617 


io-4o4232 


29 


32 


564716 


533 


968578 


83 


5 9 6i38 


616 


4o3862 


28 


33 


565o36 


533 


968528 


83 


596508 


616 


403492 


27 


34 


565356 


532 


968479 


83 


596878 


616 


4o3l22 


26 


35 


565676 


532 


968429 


83 


597247 


6i5 


402753 


25 


36 


565995 


53 1 


968379 


83 


597616 


6i5 


402384 


24 


37 


5663i4 


53 1 


968329 


83 


597985 


6i5 


40201 5 


23 


38 


566632 


53 1 


968278 


83 


598354 


614 


401646 


22 


3 9 


566951 


53o 


968228 


84 


598722 


614 


401278 


21 


4o 


567269 


53o 


96817S 


84 


599091 


6i3 


400909 


20 


4i 


9.567587 


529 


9.968128 


84 


9.599409 


6i3 


io-4oo54i 


19 


42 


567904 


529 


968078 


84 


599827 


6i3 


400173 


18 


43 


568222 


528 


968027 


84 


600194 


612 


399806 


17 


44 


568539 


5 2 8 


967977 


84 


6oo562 


612 


399438 


16 


45 


568856 


528 


967927 


84 


600929 


611 


399071 


i5 


46 


569172 


527 


967876 


84 


601296 


611 


398704 


14 


47 


56 9 488 


527 


967826 


84 


6oi663 


611 


3 9 8337 


i3 


48 


569804 


526 


967775 


84 


602029 


610 


397971 


12 


49 


570120 


5a6 


967725 


84 


602393 


610 


397605 


11 


5o 


570435 


525 


967674 


84 


602761 


610 


397239 


10 


5i 


9-570751 


525 


9-967624 


84 


9>6o3i27 


609 


10-396873 


9 


52 


D7 1 066 


524 


967573 


84 


60349.3 


609 


396507 


8 


53 


571380 


524 


967522 


85 


6o3858 


609 


396142 


7 


54 


571695 


523 


967471 


85 


604223 


608 


395777 


6 


55 


572009 


523 


967421 


85 


6o4588 


608 


3g54i2 


5 


56 


572323 


523 


967370 


85 


604953 


607 


395047 


4 


57 


572636 


522 


967319 


85 


6o53i7 


607 


3 9 4683 


3 


58 


572950 


522 


967268 


85 


6o5682 


607 


394318 


2 


8 5 9 


573263 


521 


967217 


85 


606046 


606 


393954 


1 


1 6 ° 


573570 


. 521 


967166 


85 


606410 


606 


393390 




1 


I ' 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


§ 11] 

















(V8° 



•- 



40 


LOGARITHMIC SINES, 


TANGENTS, ETC. Table II. 


22 c 














157° 


i 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


r 


o 


9.573575 


521 


9.967166 


85 


9*606410 


606 


I0'393590 


60 


i 


573888 


520 


9671 1 5 


85 


606773 


606 


393227 


5 9 


2 


574200 


520 


967064 


85 


607137 


6o5 


392863 


58 


3 


5745l2 


5ig 


967013 


85 


607500 


6o5 


3925oo 


5 7 


4 


574824 


519 


966961 


85 


607863 


604 


392137 


56 


5 


575i36 


519 


966910 


85 


600225 


604 


391775 


55 


6 


575447 


5i8 


966859 


85 


6o8588 


604 


391412 


54 


7 


575 7 58 


5i8 


966808 


85 


608950 


6o3 


39Io5o 


53 


8 


576069 


5i 7 


966756 


86 


609312 


6o3 


3 9 o688 


52 


9 


576379 


5i 7 


966705 


86 


609674 


6o3 


390326 


5i 


10 


576689 


5i6 


966653 


86 


6ioo36 


602 


389964 


5o 


ii 


9.576999 


5i6 


9.966602 


86 


9-610397 


602 


IO.389603 


49 


12 


577309 


5i6 


96655o 


86 


610769 


602 


389241 


48 


i3 


577618 


5i5 


966499 


86 


611120 


601 


38888o 


47 


U 


577927 


5i5 


966447 


86 


61 1480 


601 


388520 


46 


i5 


5 7 8236 


5i4 


966395 


86 


61 1 84i 


601 


388i59 


45 


16 


578545 


5i4 


966344 


86 


612201 


600 


387799 


44 


17 


578853 


5i3 


966292 


86 


6i256i 


600 


387439 


43 


18 


579162 


5i3 


966240 


86 


612921 


600 


387079 


42 


19 


579470 


5i3 


966188 


86 


613281 


5 99 


386719 


4i 


20 


579777 


5l2 


966136 


86 


6i364i 


5 99 


38635 9 


4o 


21 


9 .58oo85 


5l2 


9-966085 


87 


9-614000 


5 9 8 


io-386ooo 


3 9 


22 


580392 


5u 


966o33 


87 


614359 


5 9 8 


385641 


38 


23 


580699 


5u 


965981 


87 


614718 


5 9 8 


385282 


37 


24 


58ioo5 


5u 


965928 


87 


615077 


5 97 


384923 


36 


25 


58i3i2 


5io 


965876 


87 


6i5435 


5 97 


384565 


35 


26 


58i6i8 


5io 


965824 


87 


6i5 79 3 


5 97 


384207 


34 


27 


581924 


509 


965772 


87 


616161 


5 9 6 


383849 


33 


28 


582229 


509 


965720 


87 


616509 


5 9 6 


383491 


32 


29 


582535 


509 


9 65668 


87 


616867 


5 9 6 


383i33 


3i 


3o 


582840 


5o8 


9656i5 


87 


617224 


5 9 5 


382776 


3o 


3i 


9 -583 i45 


5o8 


9.965363 


87 


9.617582 


5 9 5 


10.382418 


29 


32 


583449 


507 


9655i 1 


87 


617939 


5 9 5 


382061 


28 


33 


583754 


507 


965458 


87 


618295 


594 


381705 


27 


34 


584o58 


5o6 


965406 


87 


6i8652 


594 


38i348 


26 


35 


58436i 


5o6 


9 65353 


88 


619008 


594 


380992 


25 


36 


584665 


5o6 


9653oi 


88 


6i 9 364 


5 9 3 


38o636 


24 


37 


584968 " 


5o5 


965248 


88 


619720 


5 9 3 


380280 


23 


38 


585272 


5o5 


965195 


88 


620076 


5 9 3 


379924 


22 


3 9 


585574 


5o4 


965143 


88 


620432 


592 


379568 


21 


4o 


585877 


5o4 


960090 


88 


620787 


592 


379213 


20 


4i 


9-586179 


5o3 


9-965037 


88 


9-621142 


592 


10-378858 


19 


42 


586482 


5o3 


964984 


88 


621497 


591 


3785o3 


18 


43 


586783 


5o3 


964931 


88 


62i852 


591 


378148 


17 


44 


58 7 o85 


5o2 


964879 


88 


622207 


590 


377793 


16 


45 


587386 


502 


964826 


88 


622561 


590 


37743q 


i5 


46 


58 7 688 


5oi 


964773 


88 


622915 


590 


377085 


14 


47 


587989 


5oi 


964720 


88 


623269 


58 9 


376731 


i3 


48 


588289 


5oi 


964666 


89 


62362J 


58 9 


376377 


12 


P 


5885 9 o 


5oo 


964613 


89 


623976 


58 9 


376024 


11 


5o 


588890 


5oo 


964560 


89 


624330 


588 


375670 


10 


5i 


9.589190 


499 


9.964507 


89 


9-624683 


588 


10.375317 





52 


589489 


499 


964454 


89 


625o36 


588 


374964 


8 


53 


589780 


499 


964400 


89 


625388 


58 7 


374612 


7 


54 


590088 


4 9 B 


964347 


89 


625741 


587 


374259 


6 


55 


590387 


498 


964294 


89 


626093 


58 7 


373907 


5 


56 


5 9 o686 


497 


964240 


89 


626445 


586 


373555 


4 


ll 


590984 


497 


964187 


89 


626797 


586 


373203 


3 


591282 


497 


964133 


89 


627149 


586 


372851 


2 


5 9 


591580 


496 


964080 


89 


627501 


585 


372499 


1 


60 


591878 


496 


964026 


89 


627852 


585 


372148 





/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


/ 


112 















i 


>7° 



Table II. LOGARITHMIC SINES, 


TANGENTS, ETC 


41 


23° 














156° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


/ 





9.591878 


496 


9-964026 


£9 


9-627852 


585 


IO'372i48 


60 


i 


592176 


495 


963972 


89 


620203 


585 


371797 


5 9 


2 


592473 


495 


9639J9 


89 


628554 


585 


371446 


58 


3 


592770 


495 


9 63865 


90 


628905 


584 


371093 


57 


4 


593067 


494 


9 638n 


90 


629255 


584 


370745 


56 


5 


5 9 3363 


494 


963757 


90 


629606 


583 


370394 


55 


6 


593659 


493 


963704 


90 


629956 


583 


370044 


54 


7 


593955 


493 


96365o 


90 


63o3o6 


583 


369694 


53 


8 


594251 


493 


963596 


90 


63o656 


583 


36o344 


52 


9 


594547 


492 


963542 


90 


63ioo5 


582 


368995 


5i 


10 


594842 


492 


963488 


90 


63i355 


582 


368645 


5o 


ii 


9-595137 


491 


9-963434 


90 


9-631704 


582 


10-368296 


49 


12 


595432 


491 


963379 


90 


632o53 


58i 


367947 


48 


i3 


595727 


491 


96332!) 


90 


632402 


58i 


367598 


47 


i4 


596021 


490 


963271 


90 


632750 


58 1 


367200 


46 


i5 


5963 1 5 


490 


963217 


90 


633099 


58o 


366901 


45 


16 


596609 


489 


963163 


90 


633447 


58o 


366553 


44 


n 


596903 


489 


963108 


9' 


633793 


58o 


3662o5 


43 


18 


597196 


489 


963o54 


9 1 


634U3 


579 


365857 


42 


19 


597460 


488 


962999 


9 1 


634490 


579 


3655io 


4i 


20 


5 977 83 


488 


962945 


9 1 


634838 


579 


365i62 


4o 


21 


9-598075 


487 


9-962890 


9 1 


g-635i85 


5 7 8 


io-3648i5 


3 9 


22 


5 9 8368 


487 


962836 


9 1 


635532 


5 7 8 


364468 


38 


23 


5 9 866o 


487 


962781 


9 1 


6358 7 9 


5 7 e 


364121 


37 


24 


598952 


486 


962727 


9 1 


636226 


577 


363774 


36 


25 


599244 


486 


962672 


9 1 


636572 


577 


363428 


35 


26 


599536 


485 


962617 


9 1 


636919 


577 


363o8i 


34 


27 


599827 


485 


962562 


9 1 


637265 


577 


362735 


33 


28 
1 29 

3o 


6001 18 


485 


962508 


9 1 


63761 1 


5 7 6 


36238 9 


32 


600409 


484 


962453 


9 1 


637956 


576 


362044 


3i 


600700 


484 


962398 


92 


638302 


576 


36i6 9 8 


3o 


3i 


9-600990 


484 


9-962343 


92 


9.638647 


5 7 5 


io-36i353 


29 


32 


601280 


483 


962288 


92 


638992 


575 


36ioo8 


28 


33 


601570 


483 


962233 


92 


639337 


5 7 5 


36o663 


27 


34 


601860 


482 


962178 


92 


639682 


574 


36o3i8 


26 


35 


602 1 5o 


482 


962123 


92 


640027 


574 


359973 


25 


36 


6o243o 


482 


962067 


92 


640371 


574 


359629 


24 


37 


602728 


481 


962012 


92 


640716 


573 


359284 


23 


38 


603017 


481 


961957 


92 


641060 


573 


358 9 4o 


22 


3 9 


6o33o5 


481 


961902 


92 


641404 


573 


3585 9 6 


21 


40 


603594 


480 


961846 


92 


641747 


572 


358253 


20 


4i 


9-6o3882 


480 


9.961791 


92 


9-642091 


572 


10-357909 


10 


42 


604170 


479 


961735 


92 


642434 


572 


357366 


10 


43 


604457 


479 


961680 


92 


642777 


572 


357223 


17 


44 


604745 


479 


961624 


93 


643 1 20 


571 


35688o 


16 


45 


6o5o32 


478 


961569 


93 


643463 


571 


356537 


i5 


46 


6o53i9 


478 


96i5i3 


93 


6438o6 


5 7 i 


356194 


14 


47 


6o56o6 


478 


961458 


93 


644U8 


570 


355852 


i3 


48 


605892 


477 


961402 


93 


644490 


570 


3555io 


12 


49 


606179 


477 


961346 


93 


644832 


570 


355i68 


11 


5o 


6o6465 


476 


961290 


93 


645174 


56 9 


354826 


10 


5i 


9-606751 


476 


9-961235 


93 


9-6455i6 


56 9 


10-354484 


Q 


52 


607036 


476 


961179 


9 3 


645857 


56 9 


354U3 


8 


53 


607322 


473 


96 1 1 2 3 


93 


646 1 99 


56 9 


3538oi 


7 


54 


607607 


475 


961067 


93 


646540 


568 


35346o 


6 


55 


607892 


474 


961011 


93 


646881 


568 


353no 


5 


56 


608177 


474 


960955 


93 


647222 


568 


352778 


4 


57 


608461 


474 


960899 


93 


647562 


567 


352438 


3 


58 


608745 


473 


960843 


94 


647903 


567 


352097 


2 


5 9 


609029 


473 


960786 


94 


648243 


567 


351767 


1 


60 


609313 


473 


960730 


94 


648583 


566 


35i4i7 





/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


1 


11 


30 












66° 



42 


LOGARITHMIC SINES, 


TANGENTS, ETC 


Table II. 


24° 














155° 


r 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D.« 


Cotang. 


/ 





9-609313 


473 


9*960730 


94 


9-648583 


566 


I0'35i4i7 


60 


I 


, 609597 


472 


960674 


9 4 


648923 


566 


351077 


5 9 


2 


609880 


472 


960618 


9 4 


649263 


566 


350737 


58 


3 


610164 


472 


96o56l 


9 4 


649602 


566 


35o3 9 8 


57 


4 


610447 


471 


96o5o5 


9 4 


649942 


565 


35oo58 


56 


5 


610729 


471 


960448 


94 


65o28i 


565 


349719 


55 


6 


611012 


470 


960392 


94 


660620 


565 


34938o 


54 


7 


61 1 294 


470 


96o335 


94 


660959 


564 


349041 


53 


8 


6n5 7 6 


470 


960279 


94 


651297 


564 


348703 


52 


9 


6n858 


469 


960222 


94 


65i636 


564 


348364 


5i 


10 


612140 


469 


960165 


94 


651974 


563 


348026 


5o 


ii 


9-612421 


469 


9-960109 


96 


9-6523i2 


563 


10-347688 


49 


12 


612702 


468 


960052 


9 5 


65265o 


563 


34735o 


48 


i3 


612983 


468 


939995 


96 


652988 


563 


347012 


47 


i4 


6i3264 


467 


959938 


9 5 


653326 


562 


346674 


46 


i5 


6i3545 


467 


9 5 9 882 


9 5 


653663 


562 


346337 


45 


16 


6i3825 


467 


959825 


9 5 


654ooo 


562 


346000 


44 


n 


6i4i65 


466 


959768 


9 5 


654337 


56 1 


345663 


43 


18 


6i4385 


466 


9 5 9 7l I 


9 5 


654674 


56i 


345326 


42 


19 


6i4665 


466 


909654 


9 5 


655ou 


56i 


344989 


4i 


1 20 


614944 


465 


959596 


9 5 


655348 


56i 


344652 


4o 


21 


9-6i5223 


465 


9-959539 


9 5 


9-655684 


56o 


io- 3443 1 6 


3 9 


22 


6i55o2 


465 


959482 


9 5 


656o2o 


56o 


343980 


38 


23 


6i5 7 8i 


464 


959425 


95 


.656356 


56o 


343644 


37 


24 


616060 


464 


9 5 9 368 


9 5 


656692 


55 9 


3433o8 


36 


25 


6i6338 


464 


959310 


96 


657028 


55 9 


342972 


35 


26 


616616 


463 


959253 


96 


657364 


55 9 


342636 


34 


27 


616894 


463 


959195 


96 


667699 


55 9 


3423oi 


33 


20 


617172 


462 


959138 


96 


658o34 


558 


341966 


32 


29 


617450 


462 


959080 


96 


65836 9 


558 


34i63i 


3i 


3o 


617727 


462 


959023 


96 


658704 


558 


341296 


3o 


3i 


9-618004 


461 


9-958965 


96 


9.659039 


558 


10-340961 


29 


32 


618281 


461 


958908 


96 


659370 


557 


340627 


28 


33 


6i8558 


461 


9 5885o 


96 


659708 


557 


340292 


27 


34 


6i8834 


460 


968792 


96 


660042 


557 


339968 


26 


35 


619110 


460 


958734 


66 


660376 


55 7 


339624 


25 


36 


6i 9 386 


460 


958677 


96 


660710 


556 


339290 


24 


37 


619662 


45g 


958619 


96 


66io43 


556 


338967 


23 


38 


6i 99 38 


459 


968361 


96 


661377 


556 


338623 


22 


3 9 


620213 


459 


9585o3 


97 


661710 


555 


3382QO 


21 


4o 


620488 


458 


958445 


97 


662043 


555 


337967 


2C 


4i 


9-620763 


458 


9-958387 


97 


9-662376 


555 


10-337624 


1Q 


42 


62io38 


457 


958329 


97 


662709 


554 


337291 


10 


43 


62i3i3 


457 


958271 


97 


663o42 


554 


336 9 58 


17 


44 


621587 


437 


9582i3 


97 


663375 


554 


336625 


16 


45 


621861 


456 


958 1 54 


97 


663707 


554 


336293 


i5 


46 


622i35 


456 


958096 


97 


664039 


553 


335961 


14 


47 


622409 


456 


968038 


97 


664371 


553 


335629 


i3 


48 


622682 


455 


967979 


97 


664703 


553 


336297 


12 


49 


622956 


455 


957921 


97 


665o35 


553 


334965 


11 


5o 


623229 


455 


967863 


97 


665366 


552 


334634 


10 


5 1 


9-6235o2 . 


454 


9-957804 


97 


9.665698 


552 


io-3343o2 





52 


623774 


454 


957746 


98 


666029 


552 


333971 


8 


53 


624047 


454 


957687 


98 


66636o 


55i 


333640 


7 


54 


624319 


453 


957628 


98 


666691 


55i 


333309 


6 


55 


624391 


453 


957670 


98 


667021 


55i 


332979 


5 


56 


624863 


453 


967611 


98 


667352 


55 1 


332648 


4 


57 


625i35 


452 


967452 


98 


667682 


55o 


3323i8 


3 


58 


625406 


452 


967393 


98 


668oi3 


55o 


331987 


2 


5 9 


625677 


452 


957335 


98 


668343 


55o 


33i657 


1 


60 


625948 


45i 


967276 


98 


668673 


55o 


33i327 





1 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


t 


114 


1° 












65° 



Table II. LOGARITHMIC SINES, 


TANGENTS, ETC. 


* 


25 c 


> 












154° J 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


t 1 





9-625948 


45 1 


9.957276 


9? 


9.668673 


55o 


io-33i327 


60 


i 


626219 


45 1 


907217 


98 


669002 


549 


330998 


5 9 


2 


626490 


45 1 


9 57i58 


98 


669332 


549 


33o668 


58 


3 


626760 


45o 


957099 


^ 


669661 


549 


33o339 


57 


4 


627030 


45o 


957040 


98 


669991 


548 


330009 


56 


5 


627800 


45o 


956981 


98 


670320 


548 


329680 


55 3 


6 


627570 


449 


956921 


99 


670649 


548 


32935i 


54 | 


7 


627840 


449 


956862 


99 


670977 


548 


329023 


53 j 


8 


628109 


440 


9568o3 


99 


671306 


547 


328694 


52 § 


9 


628378 


448 


956744 


99 


67i635 


547 


328365 


5i I 


IO 


628647 


448 


956684 


99 


671963 


547 


328037 


5o 1 


ii 


9-628916 


457 


9-906625 


99 


9-672291 


547 


10-327709 


40 I 


12 


629185 


447 


956566 


99 


672619 


546 


327381 


48 I 


i3 


629453 


447 


906506 


99 


672947 


546 


327053 


47 


U 


629721 


446 


956447 


99 


673274 


546 


326726 


46 


i5 


629989 


446 


956387 


99 


673602 


546 


3263 9 8 


45 


16 


630257 


446 


956327 


99 


673929 


545 


326071 


44 


17 


63o524 


446 


956268 


99 


674257 


545 


325743 


43 


18 


630792 


445 


906208 


100 


674584 


545 


3254i6 


42 


«9 


63 1 059 


445 


956148 


100 


6749 I I 


544 


325089 


4i 


20 


63i326 


445 


956089 


100 


675237 


544 


324763 


4o 


21 


9 -63 1 593 


444 


9-936029 


100 


9-675564 


544 


10-324436 


3 9 


22 


63 1 85g 


444 


955969 


100 


675890 


544 


324110 


38 


23 


632I2D 


444 


955909 


100 


676217 


543 


323 7 83 


37 


i 24 


632392 


443 


935849 


100 


676543 


543 


323457 


36 


25 


632658 


443 


955789 


100 


676869 


543 


323i3i 


35 


26 


632923 


443 


955729 


100 


677194 


543 


322806 


34 


27 


633 1 89 


442 


955669 


100 


677520 


542 


322480 


33 


28 


633454 


442 


935609 


100 


677846 


542 


322i54 


32 


29 


633719 


442 


955548 


100 


678171 


542 


321829 


3i 


3o 


633 9 84 


44 1 


955488 


ICO 


678496 


542 


32i5o4 


3o 


3i 


9-634249 


44i 


9-955428 


101 


9-678821 


54i 


IO-32H79 


29 


32 


6345i4 


44o 


9 55368 


101 


679146 


54i 


32o854 


28 


33 


634778 


44o 


955307 


101 


679/71 


54i 


320529 


27 


34 


635o42 


44o 


955247 


101 


679795 


54i 


320200 


26 | 


35 


6353o6 


439 


955i86 


101 


680120 


54o 


319880 


25 1 


36 


635570 


439 


955126 


101 


68o444 


54o 


319556 


24 1 


37 


635834 


439 


955o65 


101 


680768 


54o 


319232 


23 


38 


636097 


438 


955oo5 


101 


681092 


54o 


318908 


22 


3 9 


63636o 


438 


954944 


101 


681416 


53 9 


3i8584 


21 


4o 


636623 


438 


9 54383 


101 


681740 


539 


318260 


20 


41 


9-636886 


437 


9-954823 


101 


9-682o63 


53 9 


10.317937 


19 


42 


637148 


437 


954762 


101 


682387 


53 9 


3i 7 6i3 


10 


43 


63741 1 


437 


954701 


101 


682710 


538 


317290 


17 


44 


637673 


437 


954640 


101 


683o33 


538 


316967 


16 


45 


637935 


436 


954579 


101 


683356 


538 


3i6644 


i5 


46 


638197 


436 


954018 


102 


683679 


538 


3i632i 


14 


47 


638458 


436 


954457 


102 


684001 


537 


3 1 5999 


i3 


43 


638720 


435 


954396 


102 


684324 


53 7 


315676 


12 


4 9 


6.38981 


435 


954335 


102 


684646 


53 7 


3i5354 


11 


5o 


639242 


435 


934274 


102 


684968 


53 7 


3i5o32 


10 


5i 


9-6395o3 


434 


9-954213 


162 


9-685290 


536 


io-3i47io 


9 


52 


639764 


434 


954152 


102 


685612 


536 


3i4388 


8 


53 


640024 


434 


954090 


102 


685934 


536 


3 1 4066 


7 


54 


640284 


433 


954029 


102 


686255 


536 


3i3745 


6 


55 


64o544 


433 


953968 


102 


686577 


535 


3i3423 


5 


56 


640804 


433 


953906 


102 


686898 


535 


3i3io2 


4 


57 


641064 


432 


953845 


102 


687219 


535 


312781 


3 


58 


64i324 


432 


953783 


102 


687540 


535 


312460 


2 


5 9 


641 583 


432 


953722 


io3 


687861 


534 


3i2i3 9 


1 


60 


641842 


43 y 


95366o 


io3 


688182 


534 


3ii8i8 





/ 
lie 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


'! 















1 


w ii 



44 


LOGARITHMIC SINES, 


TANGENTS, ETC. Table II. j 


26° 














153° 


i 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


t 


'0 


9-641842 


43 1 


9-95366o 


io3 


9-688182 


534 


io-3ii8i8 


60 


i 


642 I 01 


43 1 


953599 


io3 


6885o2 


534 


311498 


5 9 


2 


64236o 


43 1 


953537 


io3 


688823 


534 


3i 1 177 


58 


3 


642618 


43o 


953475 


io3 


689143 


533 


3io857 


57 


4 


642877 


43 


9534l3 


io3 


68 9 463 


533 


3io537 


56 


5 


643 1 35 


43o 


953352 


io3 


689783 


533 


310217 


55 


6 


643393 


43o 


953290 


io3 


690103 


533 


309897 


54 


7 


64365o 


429 


953228 


io3 


690423 


533 


309577 


53 


8 


643908 


429 


9o3i66 


io3 


690742 


532 


3o 9 258 


52 


9 


644i65 


429 


953io4 


io3 


691062 


532 


3o8 9 38 


5i 


10 


644423 


428 


953042 


io3 


6 9 i38i 


532 


308619 


5o 


ii 


9.644680 


428 


9-952980 


104 


9-691700 


53 1 


io-3o83oo 


4o 


12 


644936 


428 


952918 


io4 


692019 


53 1 


307981 


48 


i3 


645193 


427 


9 52855 


104 


6 9 2338 


53 1 


307662 


47 


14 


64545o 


427 


952793 


104 


692656 


53 1 


307344 


46 


i5 


645706 


427 


952731 


104 


692975 


53 1 


307025 


45 


16 


645962 


426 


952669 


104 


693293 


53o 


306707 


44 


17 


646218 


426 


952606 


104 


693612 


53o 


3o6388 


43 


18 


646474 


426 


952544 


104 


693930 


53o 


306070 


42 


19 


646729 


425 


952481 


104 


694248 


53o 


3o5752 


4i 


20 


646984 


425 


952419 


104 


694566 


529 


3o5434 


4o 


21 


9-647240 


425 


9-952356 


104 


9.694883 


529 


io-3o5ii7 


39 


22 


647494 


424 


952294 


104 


695201 


529 


304799 


38 


23 


647749 


424 


95223i 


104 


6 9 55i8 


529 


304482 


37 


24 


648004 


424 


9 52i68 


io5 


6 9 5836 


529 


3 04 1 64 


36 


25 


648258 


424 


952106 


io5 


696153 


528 


3o3847 


35 


26 


6485i2 


423 


952043 


io5 


696470 


5 2 8 


3o353o 


34 


27 


648766 


423 


951980 


io5 


696787 


528 


3o32i3 


33 


20 


649020 


423 


9 5ioi 7 


io5 


697103 


5 2 8 


302897 


32 


29 


649274 


422 


95i854 


io5 


697420 


527 


3o258o 


3i 


3o 


649527 


422 


951791 


io5 


697736 


527 


302264 


3o 


3i 


9-649781 


422 


9-951728 


io5 


9.698053 


527 


10-301947 


29 


32 


65oo34 


422 


95i665 


io5 


6 9 836 9 


527 


3oi63i 


28 


33 


650287 


421 


951602 


io5 


6 9 8685 


526 


3oi3i5 


27 


34 


65o539 


421 


95i539 


io5 


699001 


526 


300999 


26 


35 


650792 


421 


951476 


io5 


699316 


526 


3oo684 


25 


36 


65 1 044 


420 


951412 


io5 


699632 


526 


3oo368 


24 


37 


651297 


420 


951349 


106 


699947 


526 


3ooo53 


23 


38 


65 1 549 


420 


9 5i286 


106 


700263 


525 


299737 


22 


3 9 


65i8oo 


419 


951222 


106 


700578 


525 


299422 


21 


40 


652o52 


419 


95i 159 


106 


700893 


525 


299107 


20 


4i 


9-6523o4 


419 


9-951096 


106 


9.701208 


524 


10-298792 


IO 


42 


652555 


418 


95io32 


106 


70i523 


524 


298477 


18 


43 


6528o6 


418 


950968 


106 


701837 


524 


298163 


17 


44 


653o57 


418 


950905 


106 


702152 


524 


297848 


16 


45 


6533o8 


418 


950841 


106 


702466 


524 


297534 


i5 


46 


653558 


4i7 


950778 


106 


702781 


523 


297219 


14 


47 


6538o8 


4i7 


950714 


106 


703095 


523 


296906 


i3 


48 


654059 


4i7 


95o65o 


106 


703409 


523 


296091 


12 


|9 


634309 


416 


9 5o586 


106 


703722 


523 


296278 


11 


5o 


654558 


416 


95o522 


107 


7o4o36 


522 


295964 


10 


5i 


9 -6548o8 


416 


9>95o458 


107 


9-7o435o 


522 


io-29565o 


Q 


52 


655o58 


416 


950394 


107 


704663 


522 


295337 


8 


53 


6553o7 


4i5 


95o33o 


107 


704976 


522 


295024 


7 


54 


655556 


4i5 


950266 


107 


705290 


522 


294710 


6 


55 


6558o5 


4i5 


950202 


107 


7o56o3 


521 


294397 


5 


56 


656o54 


4i4 


95oi38 


107 


705916 


521 


294084 


4 


57 


6563o2 


4i4 


950074 


107 


706228 


521 


293772 


3 


58 


65655i 


4i4 


95ooio 


107 


706541 


521 


2934.59 


2 


5 9 


656799 


4i3 


949945 


107 


706854 


521 


293146 


1 


60 


657047 


4i3 


949881 


107 


707166 


520 


292834 





r 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


/ 


116 


° X 












63° 



Table II. LOGARITHMIC SINES, 


TANGENTS, ETC. 


45 


27 c 














152° 





Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


r 


9.657047 


4i3 


9-949881 


107 


9*707166 


520 


10-292834 


60 


i 


657295 


41 3 


949816 


107 


707478 


520 


292522 


5o 


2 


657542 


412 


949752 


107 


707790 


520 


292210 


58 


3 


657790 


412 


949688 


108 


708102 


520 


291898 


57 


4 


658o37 


412 


949623 


108 


7084U 


5i 9 


291586 


56 


5 


658284 


412 


949558 


108 


708726 


5i 9 


291274 


55 


6 


65853i 


411 


949494 


108 


709037 


5i 9 


290963 


54 


7 


658778 


411 


949429 


108 


709349 


5i 9 


29o65l 


53 


8 


659025 


411 


949364 


108 


709660 


5i 9 


290340 


52 


9 


659271 


410 


9493oo 


108 


709971 


5i8 


290029 


5i 


IO 


659517 


410 


949235 


108 


710282 


5i8 


289718 


5o 


II 


9-659763 


410 


9.949170 


108 


9.710593 


5i8 


10-289407 


49 


12 


660009 


409 


949105 


108 


710904 


5i8 


289096 


48 


i3 


660255 


409 


949040 


108 


7II2l5 


5i8 


288785 


47 


14 


66o5oi 


409 


948975 


108 


7ii525 


5i 7 


288475 


46 


i5 


660746 


409 


948910 


108 


7ii836 


5i 7 


288164 


45 


16 


660991 


408 


948845 


108 


712146 


5i7 


287854 


44 


:? 


661 236 


408 


948780 


109 


712456 


5i 7 


287544 


43 


661481 


408 


948715 


109 


712766 


5i6 


287234 


42 


19 


661726 


407 


94865o 


109 


713076 


•5i6 


286924 


4i 


20 


661970 


407 


948584 


109 


7i3386 


5i6 


286614 


4o 


21 


9-662214 


407 


9-948519 


109 


9-713696 


5i6 


io-2863o4 


3 9 


22 


662459 


407 


948454 


109 


7i4oo5 


5i6 


285 99 5 


38 


23 


662703 


406 


948388 


109 


7i43i4 


5i5 


285686 


37 


24 


662946 


406 


9 48323 


109 


714624 


5i5 


285376 


36 


25 


663190 


406 


948257 


109 


7U933 


5i5 


285067 


35 


26 


663433 


4o5 


948192 


109 


715242 


5i5 


284758 


34 


3 


663677 


4o5 


948126 


109 


7i555i 


5i4 


284449 


33 


663920 


4o5 


948060 


109 


7i586o 


5i4 


284140 


32 


29 


6641 63 


4o5 


947995 


no 


716168 


5i4 


283832 


3i 


3o 


664406 


4o4 


947929 


no 


716477 


5i4 


283523 


3o 


3i 


9-664648 


4o4 


9-947863 


no 


9-716785 


5i4 


io-2832i5 


29 


32 


664891 


404 


947797 


no 


717093 


5i3 


282907 


28 


33 


665i33 


4o3 


94773i 


no 


7 1 7401 


5i3 


282099 


27 


34 


665375 


4o3 


947665 


no 


717709 


5i3 


282291 


26 


35 


665617 


4o3 


947600 


no 


718017 


5i3 


281983 


25 


36 


66585 9 


402 


947533 


no 


7i8325 


5i3 


281675 


24 


3 7 


666100 


402 


947467 


no 


7i8633 


5l2 


281367 


23 


38 


666342 


402 


947401 


no 


718940 


5l2 


281060 


22 


3 9 


666583 


402 


947335 


no 


719248 


5l2 


280752 


21 


4o 


666824 


401 


947269 


no 


719555 


5l2 


28o445 


20 


4i 


9-667065 


4oi 


9-947203 


no 


9.719862 


5l2 


io-28oi38 


IO 


42 


667305 


401 


947i36 


in 


720169 


5n 


279831 


IO 


43 


667546 


401 


947070 


m 


720476 


5n 


279524 


17 


44 


667786 


400 


947004 


in 


720783 


5n 


279217 


16 


45 


668027 


400 


946937 


in 


721089 


5n 


27891 1 


i5 


46 


668267 


400 


946871 


in 


721396 


5n 


278604 


14 


47 


6685o6 


3 99 


946804 


m 


721702 


5io 


278298 


i3 


48 


668746 


3 99 


946738 


in 


722009 


5io 


■277991 


12 


49 


668986 


399 


946671 


in 


722316 


5io 


277685 


11 


5o 


669225 


3 99 


946604 


in 


722621 


5io 


277379 


10 


5i 


9 • 669464 


3 9 8 


9. 9 46538 


in 


9.722927 


5io 


10-277073 


9 


52 


669703 


398 


946471 


in 


723232 


509 


276768 





53 


669942 


3 9 8 


946404 


in 


723538 


509 


276462 


7 


54 


670181 


397 


946337 


in 


723844 


509 


276156 


6 


55 


670419 


397 


946270 


112 


724U9 


509 


27585i 


5 


56 


670658 


397 


946203 


112 


724454 


5o 9 


275546 


4 


57 


670896 


397 


946 1 36 


112 


724760 


5o8 


275240 


3 


58 


6711J4 


3 9 6 


946069 


112 


725o65 


5o8 


274935 


2 


5 9 


671372 


3 9 6 


946002 


112 


725370 


5o8 


274630 


1 


60 


671609 


3 9 6 


945935 


112 


725674 


5o8 


274326 





/ 


Cosine. 


D. 


Sine. 


D ' 


Cotang. 


D. 


Tang. 


1 


ir 















02° 



46 



LOGARITHMIC SINES, TANGENTS, ETC. Table II. 



28° 














151° 


/ 




Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


t 


9.671609 


3 9 6 


9'945935 


112 


9-725674 


5o8 


I0.274326 


60 


i 


671847 


395 


. 945868 


112 


725979 


5o8 


274021 


5 9 


2 


672084 


3 9 5 


9458oo 


112 


726284 


507 


273716 


58 


3 


672321 


3 9 5 


945733 


112 


726588 


507 


273412 


5 7 


4 


672558 


3 9 5 


945666 


112 


726892 


507 


273lo8 


56 


5 


672795 


3 9 4 


9455q8 


112 


727197 


507 


272803 


55 


6 


673032 


3 9 4 


94553i 


112 


727501 


507 


272499 


54 


7 


673268 


3 9 4 


945464 


Il3 


727805 


5o6 


272196 


53 


8 


6735o5 


3 9 4 


945396 


Il3 


728109 


5o6 


271891 


52 


9 


673741 


3 9 3 


945328 


n3 


728412 


5o6 


271588 


5i 


10 


673977 


3 9 3 


945261 


n3 


728716 


5o6 


271284 


5o 


ii 


9-674213 


3 9 3 


9-945193 


n3 


9.729020 


5o6 


10-270980 


% 


12 


674448 


392 


945i25 


n3 


729323 


5o5 


270677 


i3 


674684 


392 


945o58 


n3 


729626 


5o5 


270374 


47 


14 


674919 


392 


944990 


n3 


729929 


5o5 


270071 


46 


i5 


675i55 


392 


944922 


u3 


73o233 


5o5 


269767 


45 


16 


- 675390 


391 


9 44854 


n3 


73o535 


5o5 


269465 


44 


17 


675624 


391 


944786 


u3 


73o838 


5o4 


269162 


43 


18 


675859 


391 


9447i8 


n3 


731141 


5o4 


26885 9 


42 


l 9 


676094 


391 


94465o 


n3 


73i444 


5o4 


268556 


4i 


20 


676328 


390 


944582 


114 


731746 


5o4 


268254 


4o 


21 


9-676562 


390 


9-9445i4 


n4 


9.732048 


5o4 


10-267952 


3 9 


22 


676796 


390 


944446 


114 


73235i 


5o3 


267649 


38 


23 


677030 


3 9 o 


944377 


114 


732653 


5o3 


267347 


<3 7 


24 
25 


677264 


369 


944309 


114 


732955 


5o3 


267045 


36 


677498 


3 89 


944241 


114 


733257 


5o3 


266743 


35 


26 


677731 


38 9 


944172 


114 


733558 


5o3 


266442 


34 


2 1 


. 677964 


388 


944104 


114 


73386o 


502 


266140 


33 


28 


678197 


388 


944o36 


114 


734162 


502 


265838 


32 


29 


678430 


388 


943967 


114 


734463 


502 


265537 


3i 


3o 


678663 


388 


943899 


114 


734764 


502 


265236 


3o 


■3i 


9-678895 


38 7 


9-94383o 


n4 


9.735066 


502 


10-264934 


29 


32 


679128 


387 


943761 


n4 


735367 


502 


264633 


28 


33 


679360 


387 


943693 


n5 


735668 


5oi 


264332 


27 


34 


679592 


38 7 


943624 


u5 


735969 


5oi 


264o3 1 


26 


35 


679824 


386 


943555 


n5 


736269 


5oi 


263731 


25 


36 


68oo56 


386 


943486 


n5 


736570 


5oi 


26343o 


24 


37 


680288 


386 


943417 


n5 


736870 


5oi 


263i3o 


23 


38 


680519 


385 


943348 


n5 


737171 


5oo 


262829 


22 


3 9 


680750 


385 


943279 


n5 


737471 


5oo 


262529 


21 


4o 


680982 


385 


943210 


n5 


737771 


5oo 


262229 


20 


4i 


9-68i2i3 


385 


9-943i4i 


u5 


9.738071 


5oo 


10-261929 


IO 


42 


68i443 


384 


943072 


u5 


738371 


5oo 


261629 


10 


43 


681674 


384 


943oo3 


n5 


738671 


499 


261329 


*7 


44 


681905 


384 


942934 


n5 


738971 


499 


261029 


16 


45 


682135 


384 


942864 


n5 


739271 


499 


260729 


i5 


46 


682365 


383 


942795 


116 


739370 


499 


26o43o 


14 


47 


68a5 9 5 


383 


942726 


116 


7398-70 


499 


26oi3o 


i3 


48 


682825 


383 


942656 


116 


740169 


499 


259831 


12 


49 


683o55 


383 


942587 


116 


740468 


498 


259532 


11 


5o 


683284 


382 


942517 


116 


740767 


498 


259233 


10 


5i 


9 -6835i4 


382 


9-942448 


116 


9-741066 


498 


10-258934 





52 


683743 


382 


942378 


116 


74i365 


498 


258635 


8 


53 


683972 


382 


9423o8 


116 


741664 


498 


258336 


7 


54 


684201 


38i 


942239 


116 


741962 


497 


258o38 


6 


55 


68443o 


38i 


942169 


116 


742261 


497 


257739 


5 


56 


684658 


38i 


942099 


116 


742559 


497 


257441 


4 


57 


684887 


38o 


942029 


116 


742858 


497 


257142 


3 


58 


685n5 


38o 


941959 


116 


743 1 56 


497 


256844 


2 


5 9 


685343 


38o 


941889 


117 


743454 


497 


256546 


1 


60 


6855 7 i 


38o 


941819 


'i*7 


743752 


496 


256248 





' 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


/ 


\ 11S 

















61° 



Table II. LOGARITHMIC SINES, 


TANGENTS, ETC. 47 


29° 














150° 





Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


t 


9-68557I 


38o 


9.941819 


117 


9^43752 


496 


10-256248 


60 


i 


685799 


379 


941749 


117 


744o5o 


496 


255930 


5 9 


2 


686027 


379 


941679 


117 


744348 


496 


255652 


58 


3 


686254 


379 


941609 


117 


744645 


496 


255355 


5 7 


4 


686482 


3 79 


94l539 


117 


744943 


496 


255o57 


56 


5 


686709 


3 7 § 


94U69 


117 


74524o 


496 


• 254760 


55 


6 


686 9 36 


378 


941398 


117 


745538 


495 


254462 


54 


7 


687163 


3 7 8 


9 4i328 


117 


745835 


495 


254i65 


53 


8 


68 7 38 9 


378 


941258 


117 


746132 


495 


253868 


52 


9 


687616 


377 


941 187 


117 


746429 


495 


253571 


5i 


10 


687843 


377 


941117 


117 


746726 


4 9 5 


253274 


5o 


ii 


9-688069 


377 


9-941046 


118 


9-747023 


494 


10-252977 


49 | 


12 


688295 


377 


940975 


118 


7473i9 


494 


252681 


4o j 


i3 


688521 


376 


940905 


118 


747616 


494 


252384 


4 7 


U 


688747 


376 


94o834 


118 


7479i3 


494 


252087 


46 


i5 


688972 


376 


940763 


118 


748209 


494 


251791 


45 


16 


689198 


3 7 6 


940693 


118 


7485o5 


493 


251495 


44 


n 


689423 


375 


940622 


118 


748801 


493 


251199 


43 


18 


689648 


375 


94o55i 


118 


749097 


493 


250903 


42 


19 


689873 


375 


940480 


118 


749393 


493 


250607 


4i 


20 


690098 


3 7 5 


940409 


118 


749689 


493 


2303ll 


4o 


21 


9-690323 


374 


9«94o338 


118 


9-749985 


493 


io-25ooi5 


3o I 


22 


690548 


374 


940267 


118 


750281 


492 


249719 


38 | 


23 


690772 


374 


940196 


118 


750576 


492 


249424 


3 7 


24 


690996 


3 7 4 


940125 


119 


750872 


492 


249128 


36 


25 


691220 


373 


94oo54 


119 


761 167 


492 


248833 


35 


26 


691444 


3 7 3 


939982 


119 


751462 


492 


248538 


34 


27 


691668 


373 


93991 1 


119 


751757 


492 


248243* 


33 


28 


691892 


3 7 3 


939840 


119 


752o52 


491 


' 247948 


32 


29 


6921 1 5 


372 


939768 


119 


752347 


491 


247653 


3i 


3o 


692339 


372 


939697 


119 


752642 


491 


247358 


3o 


3i 


9-692562 


372 


9-939625 


119 


9 -752937 


491 


10-247063 


29 


32 


692785 


3 7 i 


939554 


119 


75323i 


491 


246769 


28 


33 


693008 


3 7 i 


939482 


119 


753526 


491 


246474 


27 


34 


693231 


3 7 i 


939410 


119 


■ 753820 


490 


246180 


26 


35 


693453 


3 7 i 


939339 


119 


754n5 


490 


245885 


25 


36 


693676 


370 


939267 


120 


754409 


490 


245591 


H 


37 


693898 


370 


939195 


120 


; 754703 


490 


245297 


23 


38 


694120 


370 


939123 


120 


754997 


490 


245oo3 


22 


39 


694342 


370 


939052 


120 


755291 


490 


' 244709 


21 


4o 


694564 


36 9 


938980 


120 


755585 


489 


2444i 5 


20 


4i 


9-694786 


36 9 


9-938908 


120 


9-755878 


489 


10-244122 


IQ 


42 


695007 


36 9 


9 38836 


120 


756172 


489 


243828 


10 


43 


695229 


36 9 


938763 


120 


756465 


489 


243535 


17 


44 
45 


695450 


368 


938691 


120 


756759 


489 


243241 


16 


695671 


368 


938619 


120 


757052" 


489 


242948 


i5 


46 


695892 


368 


938547 


120 


757345 


488 


242655 


14 


47 


6961 i3 


368 


938475 


120 


75 7 638 


488 


242362 


i3 


48 


696334 


367 


938402 


121 


75 79 3i 


488 


242069 


12 


4 9 


696554 


367 


93833o 


121 


758224 


488 


241776 


11 


5o 


696775 


367 


9 38258 


121 


758517 


488 


241483 


10 


5i 


9-696995 


36 7 


9-938i85 


121 


9.758810 


488 


10-241190 


9 


52 


697215 


366 


938u3 


121 


759102 


487 


240898 


8 


53 


607435 


366 


938040 


121 


759395 


487 


24o6o5 


7 


54 


697654 


366 


937967 


121 


759687 


487 


24o3i3 


6 


55 


697874 


366 


937895 


121 


759979 


487 


240021 


5 


56 


698094 


365 


937822 


121 


760272 


487 


239728 


4 


5 7 


6 9 83 1 3 


365 


9 3 7749 


121 


760564 


487 


23 9 436 


3 


58 


698532 


365 


937676 


121 


760856 


486 


239144 


2 


5 9 


698751 


365 


937604 


121 


761 148 


486 


238852 


1 


6o 


698970 


364 


937531 


12.1 


761439 


486 


23856i 





/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


/ 


us 


1° 












60° ( 



48 


LOGARITHMIC SINES, 


TANGENTS, ETC. Table 


n. 


30° 














149° 


f 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


t 





9-698970 


364 


9>93753i 


121 


9.761439 


486 


I0'23856i 


60 


i 


699189 


364 


937458 


122 


761731 


486 


238269 


5 9 


2 


699407 


364 


937385 


122 


762023 


486 


237977 


58 


3 


699626 


364 


937312 


122 


762314 


486 


237686 


5 7 


4 


699844 


363 


937238 


122 


762606 


485 


237394 


56 


5 


700062 


363 


937165 


122 


762897 


485 


237103 


55 


6 


700280 


363 


937092 


122 


763l88 


485 


2368i2 


54 


I 


700498 


363 


937019 


122 


763479 


485 


236521 


53 


700716 


363 


936946 


122 


763770 


485 


23623o 


52 


9 


700933 


362 


936872 


122 


764061 


485 


235939 


5i 


10 


7on5i 


362 


936799 


122 


764352 


484 


235648 


5o 


ii 


9-70i368 


362 


9-936725 


122 


9-764643 


484 


10-235357 


4Q 


12 


7oi585 


362 


936652 


123 


764933 


484 


235067 


48 


i3 


701802 


36i 


936578 


123 


765224 


484 


234776 


47 


U 


702019 


36i 


9365o5 


123 


7655l4 


484 


234486 


46 


i5 


702236 


36i 


93643i 


123 


7658o5 


484 


234195 


45 


16 


702452 


36i 


936357 


123 


766095 


484 


233905 


44 


\l 


702669 


36o 


936284 


123 


766385 


483 


2336i5 


43 


702885 


36o 


936210 


123 


766675 


483 


233325 


42 


19 


7o3ioi 


36o 


936i36 


123 


766965 


483 


233o35 


41 


20 


7o33 1 7 


36o 


936062 


123 


767255 


483 


232745 


4o 


21 


9-7o3533 


35 9 


9-935988 


123 


9-767545 


483 


10-232455 


3 9 


22 


703749 


35 9 


935914 


123 


767834 


483 


232i66 


38 


23 


703964 


35 9 


935840 


123 


768124 


482 


231876 


37 


24 


704179 


35 9 


935766 


124 


768414 


482 


23 1 586 


36 


25 


704395 


35 9 


935692 


124 


768703 


482 


231297 


35 


26 


704610 


358 


9356i8 


124 


768992 


482 


23ioo8 


34 


27 


, 704825 


358 


935543 


124 


769281 


482 


230719 


33 


28 


7o5o4o 


358 


935469 


124 


769571 


482 


230429 


32 


29 


7o5254 


358 


935393 


124 


769860 


481 


23oi4o 


3i 


3o 


705469 


357 


935320 


124 


77°i48 


481 


229852 


3o 


3i 


9«7o5683 


35 7 


9-935246 


124 


9-770437 


481 


10-229563 


29 


32 


705898 


357 


935171 


124 


770726 


481 


229274 


28 


33 


7061 1 2 


357 


935097 


124 


77ioi5 


481 


228985 


27 


34 


706326 


356 


935o22 


124 


77i3o3 


481 


228697 


26 


35 


706539 


356 


934Q48 


124 


77i5o2 


481 


228408 


25 


36 


706753 


356 


934873 


124 


771880 


480 


228120 


24 


3? 


706967 


356 


934798 


125 


772168 


480 


227832 


23 


38 


707180 


355 


934723 


125 


772457 


480 


227543 


22 


3 9 


707393 


355 


934649 


125 


77 2 745 


480 


227255 


21 


40 


707606 


355 


934574 


125 


773o33 


480 


226967 


20 


4i 


9.707819 


355 


9-934499 


125 


9-773321 


480 


10-226679 


IO 


42 


708032 


354 


934424 


125 


773608 


479 


226392 


10 


43 


708245 


354 


934349 


125 


773896 


479 


226104 


17 


44 


708458 


354 


934274 


125 


774i84 


479 


2258i6 


16 


45 


708670 


354 


934199 


125 


774471 


479 


225529 


i5 


46 


708882 


353 


934123 


125 


774759 


479 


225241 


i4 


47 


709094 


353 


934048 


125 


775046 


479 


2 24954 


i3 


48 


709306 


353 


933973 


125 


775333 


479 


224667 


12 


i 9 


709518 


353 


933898 


126 


775621 


478 


2 24379 


11 


5o 


709730 


353 


933822 


126 


775908 


478 


224092 


10 


5i 


9-70994I 


352 


9-933747 


126 


9-776105 


478 


io-2238o5 


y 


52 


7 10 1 53 


352 


933671 


126 


776482 


478 


2235i8 




53 


710364 


352 


933596 


126 


776768 


478 


223232 


7 


54 


710575 


352 


933520 


126 


777o55 


478 


222945 


6 


55 


710786 


35i 


933445 


126 


777342 


478 


222658 


5 


56 


710997 


35i 


9 3336o 


126 


777628 


477 


222372 


4 


5 7 


711208 


35i 


93329J 


126 


777915 


477 


222085 


3 


58 


71U19 


35i 


933217 


126 


778201 


477 


221799 


2 


5 9 


711629 


35o 


933i4i 


126 


778488 


477 


22l5l2 


1 


60 


71 1839 


35o 


933o66 


126 


778774 


477 


221226 





1 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


/ 


12( 


)° 












j 


>9° 



Table II. LOGARITHMIC SINES, 


TANGENTS, ETC 


). 49 J 


31° 














148° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


/ 





9-711839 


35o 


9 «933o66 


126 


9.778774 


477 


10*221226 


60 


i 


7i2o5o 


35o 


932990 


127 


779060 


477 


220940 


5 9 


2 


712260 


35o 


932914 


127 


779346 


476 


220654 


58 


3 


712469 


349 


9 32838 


127 


779632 


476 


22o368 


57 


4 


712679 


349 


932762 


127 


779918 


476 


220082 


56 


5 


712880 


349 


932685 


127 


780203 


476 


219797 


55 


6 


713098 


S49 


932609 


127 


780480 


476 


219511 


54 


I 


7i33o8 


349 


932533 


127 


780776 


476 


219225 


53 


713517 


348 


932457 


127 


781060 


476 


218940 


52 


9 


713726 


348 


93238o 


127 


78l346 


475 


2i8654 


5i 


10 


713935 


348 


9323o4 


127 


78l63l 


475 


218369 


5o 


II 


9-7UU4 


348 


9-932228 


127 - 


9.781916 


475 


10. 218084 


& 


12 


714352 


347 


932i5i 


127 


782201 


475 


217799 


i3 


7i456i 


347 


932075 


128 


782486 


475 


217514 


47 


14 


714769 


347 


931998 


128 


782771 


475 


217229 


46 


i5 


714978 


347 


931921 


128 


783o56 


475 


216944 


45 


16 


7i5i86 


347 


93i845 


128 


783341 


475 


216659 


44 


17 


715394 


346 


931768 


128 


783626 


474 


216374 


43 


18 


7i56o2 


346 


931691 


128 


783910 


474 


216090 


42 


l 9 


715809 


346 


931614 


128 


784195 


474 


2i58o5 


4i 


20 


716017 


346 


93i537 


128 


784479 


474 


2l552I 


4o 


21 


9-716224 


345 


9-931460 


128 


9-784764 


474 


io-2i5236 


3 9 


22 


716432 


345 


9 3i383 


128 


785048 


474 


214952 


38 


23 


716639 


345 


93i3o6 


128 


785332 


473 


214668 


37 


24 


716846 


345 


931229 


129 


7856i6 


473 


214384 


36 


25 


717053 


345 


93n52 


129 


785900 


473 


214100 


35 


26 


717259 


344 


931075 


129 


786184 


473 


2i38i6 


34 


27 


717466 


344 


930998 


129 


786468 


473 


2i3532 


33 


28 


717673 


344 


930921 


129 


786752 


473 


213248 


32 


29 


717879 


344 


93o843 


129 


787036 


473 


212964 


3i 


3o 


718085 


343 


930766 


129 


787319 


47? 


212681 


3o 


3i 


9-718291 


343 


9.930688 


129 


9.787603 


472 


10-212397 


29 


32 


718497 


343 


93061 1 


129 


787886 


472 


212114 


28 


33 


718703 


343 


93o533 • 


129 


788170 


472 


2ii83o 


27 


34 


718909 


343 


93o456 


129 


788453 


472 


2 1 1 547 


26 


35 


7191U 


342 


930378 


129 


78873* 


472 


211264 


25 


36 


719320 


342 


93o3oo 


i3o 


789^9 


472 


210981 


24 


37 
38 


719525 
719730 


342 
342 


93o223 
93oi45 


i3o 
i3o 


78^02 
7*9585 


471 
471 


210698 
2io4i5 


23 

22 


39 


719935 


34i 


930067 


i3o 


789868 


471 


2IOl32 


21 


40 


720140 


34i 


929989 


i3o 


790151 


471 


209849 


20 


4i 


9-720345 


341 


9-929911 


i3o 


9-790434 


471 


10-209566 


19 


42 


720549 


34i 


929833 


i3o 


790716 


471 


209284 


18 


43 


720754 


340 


929755 





790999 


471 


209001 


H 


44 


720958 


34o 


929677 


t3o 


791281 


471 


208719 


16 


45 


721162 


34o 


929599 


i3o 


79 1 563 


470 


208437 


i5 


46 


72 1 366 


34o 


929521 


i3o 


791846 


470 


2081 54 


14 


47 


721570 


34o 


929442 


i3o 


792128 


470 


207872 


i3 


48 


721774 


33 9 


92936*- 


i3i 


792410 


470 


207590 


12 


49 


721978 


33 9 


9292^6 


i3i 


792692 


470 


207308 


11 


5o 


722181 


33 9 


920*07 


i3i 


792974 


470 


207026 


10 


5i 


9-722385 


33 9 


9.0^9129 


i3i 


9-793256 


470 


10-206744 





52 


722588 


33o 


92oo5o 


i3i 


7 9 3538 


469 


206462 


8 


53 


722791 


338 


928972 


i3i 


793819 


469 


206181 


7 


54 


722994 


338 


928893 


i3i 


794101 


469 


205899 


6 


55 


723197 


338 


928815 


i3i 


794383 


469 


205617 


5 


56 


723400 


339 


928736 


i3i 


794664 


469 


205336 


4 


57 


7236o3 


3j7 


928657 


i3i 


794946 


469 


2o5o54 


3 


58 


7238o5 


337 


928578 


i3i 


795227 


469 


204773 


2 


5 9 


724007 


337 


928499 


i3i 


7955o8 


468 


204492 


1 


60 


724210 


337 


928420 


i3i 


795789 


468 


2042 1 1 





' 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


/ 


121 















58° 



50 


LOGARITHMIC SINES, 


TANGENTS, ETC 


!. Table 


II. 


32° 














147° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


/ 





9-724210 


1% 


9*928420 


l32 


9.795789 


468 


IO«2042II 


60 


i 


724412 


33 7 


928342 


l32 


796070 


468 


2o393o 


5 9 


2 


724614 


336 


928263 


l32 


79635l 


468 


2o36^9 


58 


3 


724816 


336 


928l83 


132 


796632 


468 


203368 


5 7 


4 


725017 


336 


928104 


l32 


796913 


468 


203087 


56 


5 


725219 


336 


928025 


l32 


797194 


468 


202806 


55 


6 


725420 


335 


927946 


l32 


797474 


468 


202526 


54 


7 


725622 


335 


927867 


l32 


797755 


468 


202245 


53 


8 


725823 


335 


927787 


l32 


798036 


467 


201964 


52 


9 


726024 


335 


927708 


l32 


7983l6 


467 


201684 


5i 


10 


726225 


335 


927629 


l32 


798596 


467 


201404 


5o 


ii 


9-726426 


334 


9- 927549 


l32 


9.798877 


467 


IO-20II23 


4q 


12 


726626 


334 


927470 


• i33 


799157 


467 


200843 


48 


i3 


726827 


334 


927390 


i33 


799437 


467 


2oo563 


47 


14 


727027 


334 


927310 


i33 


799717 


467 


200283 


46 


i5 


727228 


334 


927231 


i33 


799997 


466 


200003 


45 


16 


727428 


333 


927151 


i33 


800277 


466 


199723 


44 


17 


727628 


333 


927071 


i33 


8oo557 


466 


199443 


43 


18 


727828 


333 


926991 


i33 


8oo836 


466 


199164 


42 


J 9 


728027 


333 


92691 1 


i33 


801116 


466 


198884 


4i 


20 


728227 


333 


926831 


i33 


801396 


466 


198604 


4o 


21 


9-728427 
728626 


332 


9-926751 


i33 


9-801675 


466 


10-198325 


3 9 


22 


332 


926671 


i33 


801955 


466 


198045 


38 


23 


728825 


332 


926591 


i33 


802234 


465 


197766 


37 


24 


729024 


332 


9265i 1 


1 34 


8o25i3 


465 


197487 


36 


25 


729223 


33i 


926431 


1 34 


802792 


465 


197208 


35 


26 


729422 


33i 


92635i 


i34 


803072 


465 


196928 


34 


27 


729621 


33i 


926270 


1 34 


8o335i 


465 


1 96649 


33 


20 


729820 


33i 


926190 


1 34 


8o363o 


465 


196370 


32 


29 


730018 


33o 


926110 


134 


803909 


465 


1 9609 1 


3i 


3o 


730217 


33o 


926029 


1 34 


804187 


465 


i 9 58i3 


3o 


3i 


9-73o4i5 


33o 


9-925o4o 


i34 


9-804466 


464 


10-195534 


29 


32 


73o6i3 


33o 


925868 


i34 


8o4745 


464 


195255 


20 


33 


730811 


33o 


925788 


i34 


8o5o23 


464 


194977 


27 


34 


73 1 009 


329 


925707 


i34 


8o53o2 


464 


194698 


26 


35 


731206 


329 


925626 


1 34 


8o558o 


464 


194420 


25 


36 


73i4o4 


329 


9*5545 


i35 


8o585 9 


464 


194141 


24 


3i 


731602 


329 


9 2 Vi65 


i35 


806137 


464 


i 9 3863 


23 


38 


731799 


329 


925584 


135 


80641 5 


463 


193585 


22 


3 9 


731996 


328 


9253cR 


i35 


806693 


463 


193307 


21 


4o 


732193 


328 


925222 


i35 


806971 


463 


193029 


20 


4i 


9-732390 


328 


9-925141 


i35 


9-807249 


463 


10-192751 


IO 


42 


732587 


328 


925060 


i35 


807527 


463 


192473 


10 


43 


732784 


328 


924979 


m 


807805 


463 


192195 


17 


44 


732980 


327 


924897 


i3» 


8o8o83 


463 


191917 


16 


45 


733177 


327 


924816 


i35 


8o836i 


463 


191639 


1 5: 


46 


733373 


327 


924735 


i36 


8o8638 


462 


191362 


u" 


% 


733569 


327 


924654 


1 36 


808916 


462 


191084 


i3 


733765 


32 7 


924572 


1 36 


809193 


462 


190807 


12 


i 9 


733961 


326 


924491 


i36 


£09471 


462 


190529 


11 


5o 


734i57 


326 


924409 


i36 


80^748 


462 


190252 


10 


5i 


9-734353 


326 


9-924328 


i36 


9-8ioo?5 


462 


10-189975 





52 


734549 


326 


924246 


1 36 


8io3oi 


462 


189698 


8 


53 


734744 


325 


924164 


i36 


8io58o 


462 


189420 


7 


54 


734939 


325 


924083 


i36 


810857 


462 


189143 


6 


55 


735i35 


325 


924001 


136 


8ni34 


461 


188866 


5 


56 


73533o 


325 


923919 


1 36 


811410 


&i 


188590 


4 


57 


735525 


325 


923837 


i36 


81 1687 


4to 


i883i3 


3 


58 


735719 


324 


923755 


1 3 7 


81 1964 


461 


i88o36 


2 


5 9 


735914 


324 


923673 


i3 7 


812241 


461 


187759 


1 


60 


736109 


324 


923591 


i3 7 


812517 


461 


187483 





/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


/ 


125 


J° 














57° 



Table II. LOGARITHMIC SINES, 


TANGENTS, ETC 


51 


33° 














146° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


1 





9-736109 


324 


9-923591 


i3 7 


9-812517 


461 


10-187483 


60 


i 


7363o3 


324 


923509 


i3 7 


812794 


461 


187206 


5 9 


2 


736498 


324 


923427 


i3 7 


8 1 3070 


461 


186930 


58 


3 


736692 


323 


923345 


i3 7 


8i3347 


460 


186653 


57 


4 


736886 


323 


923263 


i3 7 


8i3623 


460 


186377 


56 


5 


737080 


323 


923l8l 


i3 7 


8 1 3899 


460 


186101 


55 


6 


737274 


323 


923098 


i3 7 


814176 


460 


185824 


54 


I 


737467 


323 


923oi6 


i3 7 


8i4452 


460 


185548 


53 


737661 


322 


922933 


x3 7 


814728 


460 


185272 


52 


9 


737855 


322 


922851 


i3 7 


8i5oo4 


460 


184996 


5i 


10 


738o48 


322 


922768 


x38 


8i528o 


460 


184720 


5o 


ii 


9-738241 


322 


9-922686 


i38 


9 .8i5555 


459 


io-i84445 


4o 


12 


738434 


322 


922603 


i38 


8i583i 


459 


184169 


48 


i3 


738627 


321 


922520 


i38 


816107 


459 


i838 9 3 


47 


14 


738820 


321 


922438 


i38 


8i6382 


459 


i836i8 


46 


x5 


739013 


321 


922355 


1 38 


8 1 6658 


409 


183342 


45 


16 


739206 


321 


922272 


i38 


8i6 9 33 


459 


183067 


44 


17 


739398 


321 


922189 


i38 


817209 


459 


182791 


43 


18 


739DQO 


320 


922106 


i38 


817484 


459 


182516 


42 


19 


73 97 83 


320 


922023 


i38 


817759 


45o 


182241 


4i 


20 


739975 


320 


921940 


i38 


8i8o35 


458 


i8i 9 65 


4o 


21 


9-740167 


320 


9-921857 


1 39 


9 -8i83io 


458 


10-181690 


3 9 


22 


74o359 


320 


921774 


139 


8i8585 


458 


i8i4i5 


38 


23 


74o55o 


319 


921691 


139 


818860 


458 


181 140 


37 


24 


740742 


319 


921607 


139 


819135 


458 


i8o865 


36 


25 


740934 


319 


921524 


139 


819410 


458 


180590 


35 


26 


741 1 25 


319 


921441 


139 


819684 


458 


i8o3i6 


34 


a 


74i3i6 


3io 


921357 


139 


819959 


458 


180041 


33 


741 5o8 


3i8 


921274 


139 


820234 


458 


179766 


32 


29 


741699 


3 18 


921190 


139 


82o5o8 


457 


179492 


3i 


3o 


741889 


3i8 


921107 


139 


820783 


457 


179217 


3o 


3i 


9-742080 


3i8 


9-921023 


1 3g 


9-821057 


457 


10-178943 


29 


32 


742271 


3i8 


920939 


140 


82i332 


457 


178668 


20 


33 


742462 


3i7 


920806 


140 


821606 


457 


178394 


27 


34 


742652 


3x 7 


920772 


140 


821880 


457 


178120 


26 


35 


742842 


3i7 


920688 


1 40 


822154 


457 


177846 


25 


36 


743 o3 3 


3i7 


920604 


1 40 


822429 


457 


177571 


24 


3? 


743223 


3i 7 


920520 


140 


822703 


457 


177297 


23 


38 


7434i3 


3i6 


920436 


140 


822977 


456 


177023 


22 


39 


7436o2 


3i6 


92o352 


140 


823251 


456 


176749 


21 


40 


743792 


3i6 


920268 


140 


823524 


456 


176476 


20 


4i 


9-743982 


3 16 


9-920184 


1 40 


9.823798 


456 


10-176202 


ID 


42 


744171 


3i6 


920099 


140 


824072 


456 


175928 


l8 


43 


74436i 


3i5 


920016 


140 


824345 


456 


175655 


17 


44 


74455o 


3i5 


919931 
919846 


141 


824619 


456 


I7538i 


16 


45 


744730 


3i5 


141 


824893 


456 


175107 


i5 


46 


744928 


3x5 


919762 


141 


825i66 


456 


174834 


14 


47 


745ii7 


3i5 


919677 


141 


825439 
825713 


455 


174561 


i3h 


48 


7453o6 


3i4 


919593 


141 


455 


174287 


12 


49 


745494 


3i4 


919508 


141 


825986 


455 


1740 14 


11 


5o 


745683 


3i4 


919424 


141 


826259 


455 


173741 


10 


5i 


9-745871 


3i4 


9-919339 


Ui 


9-826532 


455 


10-173468 





52 


746060 


3i4 


919254. 


141 


826805 


455 


173195 


8 


53 


746248 


3i3 


9-19169 


141 


827078 


455 


172922 


7 


54 


746436 


3i3 


919085 


141 


827351 


455 


172649 


6 


55 


746624 


3i3 


919000 


141 


827624 


455 


172376 


5 


56 


746812 


3i3 


9 i8oi5 


142 


827897 


454 


172103 


4 


57 


746999 


3i3 


9i883o 


1 42 


828170 


454 


171830 


3 


58 


747187 


3l2 


918745 


142 


828442 


454 


I7i558 


2 


5 9 


747374 


3l2 


918659 


142 


828715 


454 


171285 


1 


60 


747562 


3l2 


918574 


142 


828987 


454 


ijioi3 





/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


/ 


12 


3° 












66° 



52 


LOGARITHMIC SINES, 


TANGENTS, ETC. Table II. 


34 c 














145° 


i 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


t 





9-747562 


3l2 


9.918574 


142 


9-828987 


454 


IO-I7ioi3 


60 


i 


747749 


3l2 


918489 


142 


829260 


454 


170740 


5 9 


2 


747936 


3l2 


918404 


142 


829532 


454 


170468 


58 


3 


748123 


3u 


9 i83i8 


142 


829805 


454 


170195 


57 


4 


7483io 


3u 


918233 


142 


830077 


454 


169923 


56 


5 


748497 


3n 


918147 


142 


83o349 


453 


1 6965 1 


55 


6 


748683 


3u 


918062 


142 


83o62i 


453 


169379 


54 


I 


748870 


3n 


917976 


143 


83o8 9 3 


453 


169107 


53 


749056 


3io 


917891 


i43 


83u65 


453 


168835 


52 


9 


749243 


3io 


917805 


143 


83 1437 


453 


168563 


5i 


10 


749429 


3io 


917719 


143 


831709 


453 


168291 


5o 


ii 


9-749615 


3io 


9-917634 


143 


9-831981 


453 


10-168019 


4q 


12 


749801 


3io 


917548 


143 


832253 


453 


167747 


48 


i3 


749987 


309 


917462 


143 


832525 


453 


167475 


47 


i4 


750172 


309 


917376 


143 


832796 


453 


167204 


46 


i5 


75o358 


309 


917290 


143 


833o68 


452 


166932 


45 


16 


75o543 


309 


917204 


143 


83333o 


452 


1 6666 1 


44 


17 


750729 


3o 9 


917118 


144 


8336i 1 


452 


i6638o 


43 


18 


750914 


3o8 


917032 


144 


833882 


452 


166118 


42 


*9 


751099 


3o8 


916946 


144 


834i54 


452 


165846 


4i 


20 


' 751284 


3o8 


916859 


144 


834425 


452 


i655 7 5 


4o 


21 


9-751469 


3o8 


9-916773 


144 


9-834696 


452 


io-i653o4 


3 9 


22 


75i654 


3o8 


916687 


144 


834967 


452 


i65o33 


38 


23 


75i83 9 


3o8 


916600 


144 


835238 


452 


164762 


37 


24 


752023 


307 


9i65i4 


144 


8355o 9 


452 


1 6449 1 


36 


25 


752208 


307 


916427 


144 


835780 


45 1 


164220 


35 


26 


752392 


307 


916341 


144 


836o5i 


45 1 


163949 


34 


27 


752576 


307 


916254 


144 


836322 


45i 


163678 


33 


28 


752760 


307 


916167 


145 


8365 9 3 


45 1 


163407 


32 


29 


752944 


3o6 


916081 


145 


836864 


45i 


i63i36 


3i 


3o 


753i28 


3o6 


915994 


145 


837134 


45 1 


162866 


3o 


3i 


9-7533i2 


3o6 


9-915907 


145 


9-8374o5 


45i 


10-162595 


29 


32 


753495 


3o6 


915820 


145 


83 7 6 7 5 


45 1 


i62325 


28 


33 


753679 


3o6 


915733 


145 


837946 


45 1 


162054 


27 


34 


753862 


3o5 


915646 


145 


8382i6 


45i 


161784 


26 


35 


754046 


3o5 


915559 


145 


838487 


45o 


i6i5i3 


25 


36 


754229 


3o5 


915472 


145 


838757 


45o 


161243 


24 


u 


754412 


3o5 


9 i5385 


145 


839027 


45o 


160973 


23 


754095 


3o5 


915297 


145 


839297 


45o 


160703 


22 


39 


754778 


3o4 


915210 


145 


83 9 568 


45o 


160432 


21 


40 


754960 


3o4 


9i5i23 


146 


83 9 838 


45o 


160162 


20 


41 


9-755i43 


3o4 


9'9i5o35 


146 


9-840108 


45o 


10-159892 


IO 


42 


755326 


3o4 


914948 


146 


840378 


45o 


159622 


18 


43 


7555o8 


3o4 


914860 


146 


840648 


45o 


159352 


17 


44 


755690 


3o4 


914773 


146 


840917 


449 


i5 9 o83 


16 


45 


755872 


3o3 


9 i4685 


146 


841 187 


449 


i588i3 


i5 


46 


756o54 


3o3 


914598 


146 


841457 


449 


158543 


14 


47 


756236 


3o3 


9i45io 


146 


841727 


449 


158273 


i3 


48 


756418 


3o3 


914422 


146 


841996 


449 


1 58oo4 


12 


& 


756600 


3o3 


9U334 


146 


842266 


449 


157734 


11 


5o 


756782 


302 


914246 


147 


842535 


449 


157465 


10 


5i 


9-756963 


302 


9-9i4i58 


147 


9-842805 


449 


10-157195 


Q 


52 


757144 


302 


914070 


147 


843074 


449 


156926 


8 


53 


757326 


302 


913982 


147 


843343 


449 


1 56657 


7 


54 


757507 


302 


913894 


147 


8436i2 


44Q 


156388 


6 


55 


757688 


3oi 


9i38o6 


147 


843882 


448 


i56ii8 


5 


56 


757869 


3oi 


913718 


147 


844i5i 


448 


1 55849 


4 


57 


758000 


3oi 


9i363o 


147 


844420 


448 


i5558o 


3 


58 


75823o 


3oi 


9i354i 


147 


844689 


448 


i553ii 


2 


5 9 


75841 1 


3oi 


9i3453 


147 


844958 


448 


i55o42 


1 


60 


758591 


3oi 


913365 


147 


845227 


448 


154773 





1 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


v 


124 


.0 












55° 



Table II. LOGARITHMIC SINES, 


TANGENTS, ETC 


53 j 


35° 














144° J 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


/ 





9.758591 


3oi 


9-9i3365 


147 


9'845227 


448 


10-154773 


60 


i 


758772 


3oo 


913276 


147 


845496 


448 


1 545o4 


5 9 


2 


758952 


3oo 


913187 


148 


845764 


448 


154236 


58 


3 


759132 


3oo 


913099 


148 


846033 


448 


153967 


57 


4 


759312 


3oo 


9i3oio 


148 


846302 


448 


1 536 9 8 


56 


5 


759492 


3oo 


912922 


148 


846570 


447 


i5343o 


55 


6 


759672 


299 


912833 


148 


846839 


447 


i53i6i 


54 


7 


759852 


299 


912744 


148 


847108 


447 


152892 


53 


8 


76oo3 I 


299 


912655 


148 


847376 


447 


152624 


52 


9 


7602 1 1 


299 


912566 


148 


847644 


447 


152356 


5i 


10 


760390 


299 


912477 


148 


8479i3 


447 


152087 


5o 


ii 


9 -760569 


298 


9-912388 


148 


9.848181 


447 


io-i5i8i9 


4q 


12 


760748 


298 


912299 


149 


848449 


447 


i5i55i 


48 


i3 


760927 


298 


912210 


149 


848717 


447 


i5i283 


47 


U 


761 106 


298 


912121 


149 


848986 


447 


i5ioi4 


46 


i5 


761285 


298 


9i2o3i 


149 


849254 


447 


150746 


45 


16 


761464 


298 


91 1942 


149 


849522 


447 


150478 


44 


17 


761642 


297 


9 u853 


149 


84979° 


446 


I502IO 


43 


1.8 


761821 


297 


911763 


149 


85ooD7 


446 


149943 


42 


19 


761999 


297 


911674 


149 


85o325 


446 


149675 


41 


20 


762177 


297 


9ii584 


149 


85o5 9 3 


446 


149407 


4o 


21 


9'762356 


297 


9-911495 


149 


9 -85o86i 


446 


10-149139 


3 9 


22 


762534 


296 


9ii4o5 


149 


85 1 [29 


446 


1 4887 1 


38 


23 


762712 


296 


9ii3i5 


i5o 


85i3 9 6 


446 


148604 


37 


24 


762889 


296 


911226 


i5o 


85 1664 


446 


148336 


36 


25 


763067 


296 


911136 


i5o 


85i 9 3i 


446 


148069 


35 


26 


763245 


296 


911046 


i5o 


852199 


446 


147801 


34 


27 


763422 


296 


910956 


i5o 


852466 


446 


147534 


33 


28 


. 763600 


295 


910866 


i5o 


852733 


445 


147267 


32 


29 


763777 


295 


910776 


i5o 


853ooi 


445 


146999 


3i 


3o 


763954 


295 


910686 


i5o 


853268 


445 


146732 


3o 


3i 


9'764l3l 


295 


9-910596 


i5o 


9-853535 


445 


10-146465 


20 


32 


7643o8 


295 


9io5o6 


i5o 


853802 


445 


146 1 98 


28 


33 


764485 


294 


9io4i5 


i5o 


854069 


445 


14593 1 


27 


34 


764662 


294 


9io325 


i5i 


854336 


445 


145664 


26 


35 


764838 


294 


910235 


i5i 


8546o3 


445 


i453o7 


25 


36 


765oi5 


294 


910144 


i5i 


854870 


445 


i45i3o 


24 


37 


765191 


294 


910054 


i5i 


855i37 


445 


144863 


23 


38 


765367 


294 


909963 


i5i 


8554o4 


445 


144596 


22 


3 9 


765544 


293 


909073 


i5i 


855671 


444 


144329 


21 


4o 


765720 


293 


909782 


i5i 


855 9 38 


444 


144062 


20 


4i 


9-765896 


293 


9-909691 


i5i 


9-856204 


444 


10-143796 


IO 


42 


766072 


293 


909601 


i5i 


856471 


444 


143529 


10 


43 


766247 


293 


909510 


i5i 


856737 


444 


143263 


17 


44 


766423 


293 


909419 


i5i 


857004 


444 


142996 


16 


45 


766598 


292 


909328 


1 5.2 


857270 


444 


142730 


i5 


. 46 


766774 


292 


909.237 


1 52 


85 7 537 


444 


142463 


14 


! 47 


766949 


292 


909146 


1 52 


8578o3 


444 


142197 


i3 


: 48 


767124 


292 


909055 


1 52 


858o6 9 


444 


141931 


12 


49 


767300 


292 


908964 


l52 


858336 


444 


141664 


11 


i 5o 


767475 


291 


908873 


l52 


8586.02 


443 


141398 


10 


j 5i 


9-767649 


291 


9-908781 


l52 


9-858868 


443 


io-i4n32 





: 52 


767824 


291 


908690 


1 5.2 


859134 


443 


140866 


8 


; 53 


767999 


291 


908599 


l52 


859400 


443 


140600 


7 


54 


768173 


291 


908507 


1 5.2 


85 9 666 


443 


i4o334 


6 


55 


768348 


290 


908416 


1 53 


859932 


443 


140068 


5 


56 


768522 


290 


908324 


1 53 


860198 


443 


139802 


4 


i 5 7 


■ 768697 


290 


908233 


1 53 


860464 


443 


i39536 


3 


58 


768871 


290 


908141 


1 53 


860730 


443 


139270 


2 


5 9 


• 769045 


290 


908049 


1 53 


860995 


443 


i3ooo5 


1 


60 


769219 


290 


907958 


1 53 


861261 


443 


138739 


1 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


! 


j 12. 


5° 












54° 



54 


LOGARITHMIC SINES, 


TANGENTS, ETC 


Table II. 1 


36° 














143° I 


r 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


/ \ 





9-769210 
769393 


290 


9-907958 


i53 


9-861261 


443 


10-138739 


60 


i 


289 


907866 


1 53 


86l527 


443 


138473 


5 9 


2 


769566 


289 


907774 


1 53 


861792 


442 


138208 


58 


3 


769740 


289 


907682 


1 53 


862058 


442 


137942 


5 7 


4 


769913 


289 


907590 


1 53 


862323 


442 


137677 


56 


5 


770087 


289 


907498 


1 53 


86258 9 


442 


137411 


55 


6 


770260 


288 


907406 


1 53 


862854 


442 


137146 


54 


7 


770433 


288 


907314 


1 54 


863iio 


442 


i3688i 


53 


8 


770606 


288 


907222 


1 54 


863385 


442 


i366i5 


52 


9 


" 770779 


288 


907129 


1 54 


86365o 


442 


i3635o 


5i 


10 


770952 


288 


907037 


r44 


863915 


442 


i36o85 


5o 


ii 


9-77II25 


288 


9 • 906945 


1 54 


9.864180 


442 


io-i3582o 


4Q 


12 


771298 


287 


906852 


1 54 


864445 


442 


135555 


48 


i3 


77U70 


287 


906760 


1 54 


864710 


442 


135290 


47 


i4 


771643 


287 


906667 


1 54 


864975 


441 


i35o25 


46 


i5 


77l8l5 


287 


906576 


1 54 


865240 


441 


134760 


45 


16 


771987 


287 


906482 


1 54 


8655o5 


441 


i344q5 


44 


17 


772159 


287 


906389 


i55 


865770 


441 


1342J0 


43 


18 


77233l 


286 


906296 


i55 


866o35 


441 


133965 


42 


l 9 


7725o3 


286 


906204 


i55 


8663oo 


44i 


133700 


4i 


20 


772675 


286 


9061 1 1 


1 55 


866564 


44i 


i33436 


4o 


21 


9- 77 28 47 


286 


9-906018 


i55 


9.866829 


44i 


io-i33i7i 


3o 


22 


773018 


286 


9o5o25 


1 55 


867094 


44i 


132906 


38 


23 


773190 


286 


905832 


i55 


867358 


44i 


132642 


37 


24 


77336i 


285 


905739 


i55 


867623 


44i 


132377 


36 


25 


773533 


285 


905645 


1 55 


867887 


44i 


i32ii3 


35 


26 


773704 


285 


9o5552 


i55 


868i52 


44o 


131848 


34 


3 


773875 


285 


905459 


i55 


868416 


44o 


i3i584 


33 


774046 


285 


9o5366 


1 56 


868680 


44o 


i3i32o 


32 


29 


774217 


285 


905272 


1 56 


868945 


44o 


i3io55 


3i 


3o 


774388 


284 


905179 


1 56 


869209 


44o 


130791 


3o 


3i 


9-774558 


284 


9-9o5o85 


1 56 


9-869473 


44o 


io-i3o527 


29 


32 


774729 


284 


904992 


1 56 


869737 


44o 


i3o263 


28 


33 


774899 


284 


904898 


1 56 


870001 


44o 


129999 


27 


34 


776070 


284 


904804 


1 56 


870265 


44o 


129735 


26 


35 


775240 


284 


9047 1 1 


1 56 


870529 


44o 


1 29471 


25 


36 


775410 


283 


904617 


1 56 


870793 


44o 


129207 


24 


37 


77558o 


283 


904523 


1 56 


871067 


44o 


128943 


23 


38 


775750 


283 


904429 


i5 7 


871321 


44o 


128679 


22 


3 9 


775920 


283 


904335 


i5 7 


87i585 


44o 


128410 


21 


4o 


776090 


283 


904241 


i5 7 


871849 


439 


I28i5i 


20 


4i 


9-776259 


283 


9-904147 


1S7 


9-872112 


439 


10-127888 


19 


42 


77 6 42Q 


282 


9o4o53 


i5 7 


872376 


43 9 


127624 


18 


43 


776598 


282 


903959 


i.5 7 


872640 


43 9 


127360 


17 


44 


776768 


282 


9 o3864 


i5 7 


872903 


43 9 


127097 


16 


45 


776937 


282 


903770 


1 5 7 


873167 


43 9 


126833 


i5 


46 


777106 


282 


903676 


i5 7 


873430 


43 9 


126570 


14 


47 


777275 


281 


9o358i 


167 


873694 


43 9 


i263o6 


i3 


48 


777444 


281 


903487 


1 5 7 


873957 


43 9 


126043 


12 


49 


777613 


281 


903392 


i58 


874220 


43 9 


126780 


11 


5o 


777781 


281 


903298 


1 58 


874484 


439 


I255i6 


10 


5i 


9-77795o 


281 


9'9o32o3 


i58 


9-874747 


439 


io-i25253 





52 


778119 


281 


903 1 08 


1 58 


875010 


43 9 


124990 


b 


53 


778287 


280 


903014 


1 58 


875273 


438 


124727 


7 


54 


778455 


280 


902919 


1 58 


875537 


438 


124463 


6 


55 


778624 


280 


902824 


1 58 


875800 


438 


124200 


5 


56 


778792 


280 


902729 


1 58 


876063 


438 


123937 


4 


5 7 


778960 


280 


902634 


1 58 


876326 


438 


123674 


3 


58 


779128 


280 


902539 


i5 9 


876589 


438 


I234ii 


2 


5 9 


779295 


279 


902444 


i5 9 


876852 


438 


123148 


1 


60 


779463 


279 


902349 


i5g 


877114 


438 


122886 





t 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


' 


12* 


)° 












53° 



Table II. LOGARITHMIC SINES, 


TANGENTS, ETC. 


55 


37° 














142° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


1 





9-779463 


279 


9-902349 


1 5 9 


9-877114 


438 


10-122886 


60 


i 


779631 


279 


902253 


l5 9 


877377 


438 


122623 


5 9 


2 


779798 


279 


902 1 58 


i5 9 


877640 


438 


122360 


58 


3 


779966 


279 


902063 


1 5 9 


877903 


438 


122097 


57 


4 


78oi33 


279 


901967 


i5 9 


878165 


438 


121835 


56 


5 


78o3oo 


278 


901872 


i5 9 


878428 


438 


121572 


55 


6 


780467 


278 


901776 


1 5 9 


878691 


438 


121309 


54 


I 


780634 


278 


901681 


i5 9 


878953 


437 


1 2 1047 


53 


780801 


278 


90i585 


i5 9 


879216 


43 7 


120784 


52 


9 


780968 


278 


901490 


1 5 9 


879478 


437 


120522 


5i 


10 


781134 


278 


901394 


160 


879741 


437 


120259 


5o 


ii 


9-781301 


277 


9-901298 


160 


9-88ooo3 


437 


IO-II9997 


4q 


12 


781468 


277 


901202 


160 


880265 


437, 


II9735 


48 


1 3 


781634 


277 


901 106 


160 


88o528 


43 7 


I 19472 


47 


14 


781800 


277 


901010 


160 


880790 


437 


II921O 


46 


i5 


781966 


277 


900914 


160 


88io52 


437 


I I 8948 


45 


16 


782132 


277 


900818 


160 


88i3i4 


437 


i i 8686 


44 


17 


782298 


276 


900722 


160 


881577 


437 


1 18423 


43 


10 


782464 


276 


900626 


160 


88i83 9 


437 


118161 


42 


19 


782630 


276 


900529 


160 


882101 


437 


1 1 7899 


4i 


20 


782796 


276 


900433 


161 


882363 


436 


117637 


4o 


21 


9-782961 


276 


9-900337 


161 


9-882625 


436 


10-117375 


3 9 


22 


783127 


276 


900240 


161 


882887 


436 


1 17 1 13 


38 


23 


783292 


275 


900144 


161 


883 1 48 


436 


1 i6852 


37 


24 


783458 


275 


900047 


161 


8834io 


436 


116590 


36 


25 


783623 


275 


899951 


161 


883672 


436 


1 i6328 


35 


26 


783788 


275 


899854 


161 


883 9 34 


436 


1 16066 


34 


27 


783q53 


275 


899757 


161 


884196 


436 


n58o4 


33 


28 


784118 


275 


899660 


161 


884457 


436 


1 1 5543 


32 


29 


784282 


274 


899564 


161 


884719 


436 


n528i 


3i 


3o 


784447 


274 


899467 


162 


884980 


436 


ll5020 


3o 


3i 


9-784612 


274 


9-899370 


162 


9-885242 


436 


10-114758 


29 


32 


784776 


274 


899273 


162 


8855o4 


436 


1 14496 


28 


33 


784941 


274 


899176 


162 


885765 


436 


H4235 


27 


34 


785io5 


274 


899078 


162 


886026 


436 


113974 


26 


35 


785269 


273 


898981 


162 


886288 


436 


113712 


25 


36 


785433 


273 


898884 


162 


886549 


435 


ii345i 


24 


37 


785597 


273 


898787 


162 


8868 1 1 


435 


ii3i8 9 


23 


38 


785761 


273 


898689 


162 


887072 


435 


112928 


22 


3 9 


785925 


273 


898592 


162 


887333 


435 


1 1 2667 


21 


40 


786089 


273 


898494 


1 63 


88 7 5 9 4 


435 


1 1 2406 


20 


4i 


9-786252 


272 


9-898397 


1 63 


9-887855 


435 


io-ii2i45 


IO 


42 


786416 


272 


898299 


i63 


888116 


435 


1 1 1884 


10 


43 


786579 


272 


898202 


i63 


8883 7 8 


435 


111622 


17 


44 


786742 


272 


898104 


i63 


88863 9 


435 


iii36i 


16 


45 


786906 


272 


898006 


1 63 


888900 


435 


11 1 100 


i5 


46 


787069 


272 


897908 


1 63 


889161 


435 


1 io83g 


14 


47 


787232 


271 


897810 


i63 


889421 


435 


1 10579 


i3 


48 


787395 


271 


897712 


i63 


889682 


435 


iio3i8 


12 


49 


787557 


271 


897614 


i63 


889943 


435 


1 10057 


11 


5o 


787720 


271 


897516 


1 63 


890204 


434 


109796 


10 


5i 


9.787883 


271 


9-897418 


164 


9-890465 


434 


10-109535 


Q 


52 


788045 


271 


897320 


164 


890725 


434 


109275 


8 


53 


788208 


271 


897222 


164 


890986 


434 


109014 


7 


54 


788370 


270 


897123 


164 


891247 


434 


108753 


6 


55 


788532 


270 


897025 


164 


891507 


434 


108493 


5 


56 


788694 


270 


896926 


164 


891768 


434 


108232 


4 


n 


788856 


270 


896828 


164 


892028 


434 


107972 


3 


789018 


270 


896729 


164 


892289 


434 


1077 1 1 


2 


5 9 


789180 


270 


8 9 663 1 


164 


892549 


434 


107451 


1 


60 


789342 


269 


8 9 6532 


164 


892810 


434 


107190 





/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


/ 


12' 


1° 















56 


LOGARITHMIC SINES, 


TANGENTS, ETC 


Table II. 


38° 














141° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


60 





9-789342 


269 


9-896532 


164 


9-892810 


434 


10-107190 


i 


789004 


269 


896433 


i65 


893070 


434 


106930 


5 9 


2 


789665 


269 


8 9 6335 


i65 


893331 


434 


106669 


58 


3 


789827 


269 


896236 


i65 


893591 


434 


106409 


5 7 


4 


789988 


269 


896137 


165 


8 9 385l 


434 


106149 


56 


5 


790149 


269 


8 9 6o38 


i65 


8941 1 1 


434 


io588 9 


55 


6 


790310 


268 


895939 


i65 


894372 


434 


io5628 


54 


7 


790471 


268 


890840 


i65 


894632 


433 


io5368 


53 


8 


790632 


268 


895741 


i65 


894892 


433 


io5io8 


52 


9 


790793 


268 


895641 


i65 


895162 


433 


104848 


5i 


10 


790954 


268 


895542 


i65 


895412 


433 


104588 


5o 


ii 


9-791115 


268 


9-895443 


166 


9.895672 


433 


iO'io4328 


49 


12 


791275 


267 


895343 


166 


895932 


433 


104068 


48 


i3 


791436 


267 


895244 


166 


896192 


433 


io38o8 


47 


U 


791696 


267 


895145 


166 


896452 


433 


io3548 


46 


i5 


791757 


267 


895045 


166 


896712 


433 


io3288 


45 


16 


791917 


267 


894945 


166 


896971 


433 


103029 


44 


17 


792077 


267 


894846 


166 


897231 


433 


102769 


43 


18 


792237 


266 


894746 


166 


897491 


433 


102609 


42 


10 


792397 


266 


894646 


166 


897761 


433 


102249 


41 


20 


792557 


266 


894546 


166 


898010 


433 


101990 


4o 


21 


9-792716 


266 


9-894446 


167 


g- 898270 


433 


10-101730 


3 9 


22 


792876 


266 


894346 


167 


8 9 853o 


433 


101470 


38 


23 


793o35 


266 


894246 


167 


898789 


433 


101211 


37 


24 


793195 


265 


894146 


167 


899049 


432 


1 0095 1 


36 


25 


793354 


265 


894046 


167 


8 99 3o8 


432 


100692 


35 


26 


7935i4 


265 


893946 


167 


8 99 568 


432 


ioo432 


34 


27 


793673 


265 


893846 


167 


899827 


432 


100173 


33 


28 


793832 


265 


89374.5 


167 


900087 


432 


099913 


32 


2 9 


793991 


265 


8 9 3645 


167 


900346 


432 


099654 


3i 


3o 


7941 5o 


264 


893544 


167 


900605 


432 


099395 


3o 


3i 


9-794308 


264 


9. 893444 


168 


9-900864 


432 


10-099136 


29 


32 


794467 


264 


893343 


168 


901124 


432 


098876 


28 


33 


794626 


264 


893243 


168 


90i383 


432 


098617 


27 


34 


794784 


264 


8 9 3i42 


168 


901642 


432 


o 9 83 58 


26 


35 


794942 


264 


893041 


168 


901901 


432 


098099 


25 


36 


795101 


264 


892940 


168 


902160 


432 


097840 


24 


37 


795259 


263 


8 9 283 9 


168 


902420 


432 


097580 


23- 


38 


795417 


263 


892739 


168 


902679 


432 


097321 


22 


3 9 


795575 


263 


8 9 2638 


168 


902938 


432 


097062 


21 


4o 


795733 


263 


892536 


168 


903197 


43 1 


096803 


20 


4i 


9-795891 


263 


9-892435 


169 


9-903456 


43i 


10-096544 


10 


42 


796049 


263 


892334 


169 


903714 


43 1 


096286 


10 


43 


796206 


263 


892233 


169 


903973 


43 1 


096027 


17 


44 


796364 


262 


892132 


169 


904232 


43 1 


095768 


l6 


45 


796521 


262 


892030 


169 


904491 


43 1 


095609 


i5 


46 


796679 


262 


891929 


169 


904760 


43,i 


095250 


i4 


47 


796836 


262 


891827 


169 


9o5oo8 


43 1 


094992 


i3 


48 


796993 


262 


891726 


169 


905267 


43 1 


094733 


12 


4 9 


797 1 5o 


261 


891624 


169 


905526 


43 1 


094474 


11 


5o 


797307 


261 


891523 


170 


900785 


43 1 


094215 


10 


5i 


9.797464 


261 


9-891421 


170 


9-906043 


43 1 


10-093957 





52 


797621 


261 


891319 


170 


906302 


43 1 


093698 


8 


53 


797777 


261 


891217 


170 


906560 


43 1 


093440 


7 


54 


797934 


261 


8911 i5 


170 


906819 


43 1 


093181 


6 


55 


798091 


261 


891013 


170 


907077 


43 1 


092923 


5 


56 


798247 


261 


89091 1 


170 


907336 


43 1 


092664 


4 


5 7 


7984o3 


260 


890809 


170 


907594 


43 1 


092406 


3 


58 


798560 


260 


890707 


170 


907853 


43 1 


092147 


2 


5 9 


798716 


260 


890606 


170 


9081 1 1 


43 


091889 


1 


60 


798872 


260 


890503 


170 


908369 


43o 


ooi63i 





/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 

1 


12* 


i° 












51° 



Table IL LOGARITHMIC SINES, 


TANGENTS, ETC. 


57 


39 c 














140° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


1 


o 


9-798872 


260 


9.890503 


170 


9.908369 


43o 


IO"09i63i 


60 


i 


799028 


260 


890400 


171 


908628 


43o 


091372 


5 9 


2 


799184 


260 


890298 


171 


908886 


43o 


091114 


58 


3 


799339 


259 


890195 


171 


909144 


43o 


090856 


57 


4 


799495 


259 


890093 


171 


909402 


43o 


090598 


56 


5 


79965l 


259 


889990 


171 


909660 


43o 


090340 


55 


6 


799806 


259 


889888 


171 


909918 


43o 


090082 


54 


7 


799962 


259 


889785 


171 


910177 


43o 


089823 


53 


8 


8001 17 


259 


889682 


171 


910435 


43o 


o8 9 565 


52 


9 


800272 


258 


889579 


HI 


910693 


43o 


089307 


5i 


10 


800427 


258 


889477 


171 


9 I0 9 5l 


43o 


089049 


5o 


ii 


9«8oo582 


258 


9-889374 


172 


9-911209 


43o 


10-088791 
088533 


4Q 


12 


800737 


258 


889271 


172 


91 1467 


43o 


48 


i3 


800892 


258 


889168 


172 


911725 


43o 


088275 


47 


U 


801047 


258 


889064 


172 


911982 


43o 


088018 


46 


i5 


801201 


258 


888961 


172 


912240 


43o 


087760 


45 


16 


8oi356 


257 


888858 


172 


912498 


43o 


087502 


44 


«2 


8oi5n 


257 


888755 


172 


912706 


43o 


087244 


43 


18 


8oi665 


257 


88865i 


172 


9i3oi4 


429 


086986 


42 


19 


801819 


25-) 


888548 


172 


913271 


429 


086729 


4i 


20 


801973 


25-) 


888444 


I 7 3 


913529 


429 


086471 


4o 


21 


9-802128 


257 


9-888341 


l 7 3 


9.913787 


429 


io-o862i3 


3 9 


22 


802282 


256 


888237 


I 7 3 


914044 


429 


085956 


38 


23 


802436 


256 


888 1 34 


I 7 3 


914302 


429 


085698 


37 


24 


8o258o 
802740 


256 


888o3o 


I 7 3 


914360 


429 


o8544o 


36 


25 


256 


887926 


I 7 3 


9U817 


429 


o85i83 


35 


26 


802897 


256 


887822 


I 7 3 


915075 


429 


084925 


34 


27 


8o3o5o 


256 


887718 


l 7 3 


9i5332 


429 


084668 


33 


28 


8o32o4 


256 


887614 


l 7 3 


915590 


429 


084410 


32 


29 


8o3357 


255 


887510 


I 7 3 


9 1 5847 


429 


0841 53 


3i 


3o 


8o35u 


255 


887406 


174 


916104 


429 


o838 9 6 


3o* 


3i 


9-8o3664 


255 


9-887302 


174 


9.916362 


429 


io-o83638 


29 


32 


803817 


255 


887198 


174 


916619 


429 


o8338i 


28 


33 


803970 


255 


887093 


174 


916877 


429 


o83i23 


27 


34 


804123 


255 


886989 


174 


917134 


429 


082866 


26 


35 


804276 


254 


886885 


174 


917391 


429 


082609 


25 


36 


804428 


254 


886780 


174 


917648 


429 


o82352 


24 


37 


8o458i 


254 


886676 


174 


917906 


429 


082094 


23 


38 


804734 


254 


886571 


174 


9 i8i63 


428 


081837 


22 


3 9 


804886 


254 


886466 


174 


918420 


428 


o8i58o 


21 


4o 


806039 


254 


886362 


I 7 5 


918677 


428 


o8i323 


20 


4i 


9-8o5i9i 


254 


9.886257 


I 7 5 


9-918934 


428 


10-081066 


IO 


42 


8o5343 


253 


886i52 


I 7 5 


919191 


428 


080809 


l8 


43 


8o5495 


253 


886047 


I 7 5 


919448 


428 


o8o552 


17 


44 


8o5647 


253 


885 9 42 


I 7 5 


919705 


428 


080295 


16 


45 


805799 


253 


885837 


I 7 5 


919962 


428 


o8oo38 


i5 


46 


8059D1 


253 


885 7 32 


I 7 5 


920219 


428 


079781 


14 


47 


8o6io3 


253 


885627 


l 7 5 


920476 


428 


079624 


i3 


48 


806254 


253 


885522 


I 7 5 


920733 


428 


079267 


12 


49 


806406 


232 


8854i6 


l 7 5 


920990 


428 


079010 


11 


5o 


8o6557 


252 


8853 1 1 


176 


921247 


428 


078753 


10 


5i 


9-806709 


252 


9-885205 


176 


9-92i5o3 


428 


10-078497 


o 


52 


806860 


252 


885ioo 


176 


921760 


428 


078240 


8 


53 


80701 1 


252 


884994 


176 


922017 


428 


077983 


7 


54 


807163 


252 


884889 


176 


922274 


428 


077726 


6 


55 


807314 


252 


884783 


176 


92253o 


428 


077470 


5 


56 


807465 


25l 


884677 


176 


922787 


428 


077213 


4 


57 


807615 


25l 


884572 


176 


923o44 


428 


076956 


3 


58 


807766 


25l 


884466 


176 


9233oo 


428 


076700 


2 


5 9 


807917 


25l 


88436o 


176 


923557 


427 


076443 


1 


60 


808067 


25l 


884254 


177 


923814 


427 


076186 





/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


1 


125 


)° 












| 


)0° J 



3* 



58 


LOGARITHMIC SINES, 


TANGENTS, ETC 


Table II. 


40° 














139° 


i 




Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


/ 


9-808067 


25l 


9.884254 


177 


9-923814 


427 


IO.076186 


60 


i 


808218 


25l 


884U8 


177 


924070 


427 


075930 


5 9 


2 


8o8368 


25l 


884042 


177 


924327 


427 


075673 


58 


3 


808519 


25o 


883 9 36 


177 


924583 


427 


075417 


57 


4 


808669 


25o 


883829 


177 


924840 


427 


075160 


56 


5 


808819 


25o 


883723 


177 


925096 


427 


074904 


55 


6 


808969 


25o 


883617 


177 


925352 


427 


074648 


54 


7 


8091 19 


25o 


8835io 


177 


925609 


427 


074391 


53 


8 


809269 


25o 


883404 


177 


9 25865 


427 


074i35 


52 


9 


809419 


249 


883297 


178 


926122 


427 


073878 


5i 


10 


809569 


249 


883191 


178 


926378 


427 


073622 


5o 


ii 


9-809718 


249 


9-883o84 


178 


9.926634 


427 


10-073366 


4o 


12 


809868 


249 


882977 


178 


926890 


427 


073110 


48 


i3 


810017 


249 


882871 


178 


927147 


427 


072853 


47 


U 


810167 


249 


882764 


178 


927403 


427 


072597 


46 


i5 


8io3i6 


248 


882657 


178 


927659 


427 


072341 


45 


16 


810465 


248 


88255o 


178 


927915 


427 


072085, 


44 


i-7 


810614 


248 


882443 


178 


928171 


427 


071829 


43 


18 


810763 


248 


882336 


179 


928427 


427 


07 1 57 J 


42 


l 9 


810912 


248 


882229 


179 


928684 


427 


071316 


4i 


20 


811061 


248 


882121 


179 


928940 


427 


071060 


4o 


21 


9-811210 


248 


9-882014 


179 


9-929196 


427 


10-070804 


3 9 


22 


8u358 


247 


881907 


179 


929452 


427 


070548 


38 


23 


811507 


247 


881799 


179 


929708 


427 


070292 


37 


24 


8u655 


247 


881692 


179 


029964 


426 


070006 


36 


25 


81 1804 


247 


881 584 


179 


930220 


426 


069780 


35 


26 


811952 


247 


881477 


179 


930475 


426 


069525 


34 


27 


812100 


247 


88i36 9 


179 


930731 


426 


069269 


33 


28 


812248 


247 


881261 


180 


930987 


426 


0690 1 3 


32 


29 


812396 


246 


88u53 


180 


931243 


426 


068757 


3i 


3o 


8i2544 


246 


881046 


180 


931499 


426 


o685oi 


3o 


3i 


9-812692 


246 


9-88o 9 38 


180 


9-931755 


426 


10-068245 


29 


32 


812840 


246 


88o83o 


180 


932010 


426 


067990 


28 


33 


812988 


246 


880722 


180 


932266 


426 


067734 


27 


34 


8i3i35 


246 


88061 3 


180 


932522 


426 


067478 


26 


35 


8i3283 


246 


88o5o5 


180 


932778 


426 


067222 


25 


36 


8i343o 


245 


880397 


180 


933o33 


426 


066967 


24 


37 


8i35-78 


245 


880289 


181 


933289 


426 


0667 1 1 


23 


38 


813725 


245 


880180 


181 


933545 


426 


o66455 


22 


3 9 


813872 


245 


880072 


181 


9338oo 


426 


066200 


21 


4o 


814019 


245 


879963 


181 


934o56 


426 


065944 


20 


4i 


9-814166 


245 


9-879855 


181 


9-9343ii 


426 


10-065689 


10 


42 


8i43i3 


245 


879746 


181 


934567 


426 


o65433 


18 


43 


814460 


244 


8 79 63 7 


181 


934822 


426 


065178 


17 


44 


814607 


244 


879529 


181 


935078 


426 


064922 


16 


45 


8i4753 


244 


879420 


181 


9 35333 


426 


064667 


i5 


46 


814900 


244 


8793 1 1 


181 


935589 


426 


06441 1 


14 


47 


8i5o46 


244 


879202 


182 


935844 


426 


064 1 56 


i3 


48 


8i5i 9 3 


244 


879093 


182 


936100 


426 


063900 


12 


49 


8i533 9 


244 


878984 


182 


9 36355 


426 


063645 


11 


5o 


81 5485 


243 


878875 


182 


936611 


426 


o63389 


10 


5i 


9-8i563i 


243 


9-878766 


182 


9-936866 


425 


io-o63i34 





52 


815778 


243 


878656 


182 


9371 21 


425 


062879 


8 


53 


815924 


243 


878547 


182 


937377 


425 


062623 


7 


54 


816069 


243 


878438 


182 


937632 


425 


062368 


6 


55 


8i62i5 


243 


878328 


182 


937887 


425 


o62ii3 


5 


56 


8i636i 


243 


878219 


1 83 


938142 


425 


06 1 858 


4 


57 


8i65o7 


242 


878109 


1 83 


9 383o8 


425 


061602 


3 


58 


8i6652 


242 


877999 


1 83 


9 38653 


425 


061347 


2 


5 9 


816798 


242 


877890 


1 83 


938908 


425 


061092 


1 


60 


816943 


242 


877780 


1 83 


939163 


425 


060837 





/ 


Cosine. 


** 


Sine. 


D. 


Cotang. 


D. 


Tang. 


/ 


18( 


)° 












49° 



Table II. LOGARITHMIC SINES, 


TANGENTS, ETC. 


59 


41° 














138° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


1 


o 


9.816943 


242 


9.877780 


1 83 


9.939163 


425 


10-060837 


60 


i 


817088 


242 


877670 


1 83 


939418 


425 


o6o582 


5 9 


2 


817233 


242 


877560 


1 83 


939673 


425 


060327 


58 


o 


817379 


242 


877450 


1 83 


939928 


425 


060072 


57 


4 


817524 


241 


877340 


1 83 


940183 


425 


059817 


56 


5 


817668 


241 


877230 


184 


940439 


425 


059561 


55 


6 


817813 


241 


877120 


184 


940694 


425 


059306 


54 


7 


817958 


241 


877010 


184 


940949 


425 


059051 


53 


8 


8i8io3 


241 


876899 


184 


941204 


425 


050796 


52 


9 


818247 


241 


876789 


184 


94U59 


425 


•o5854i 


5i 


10 


818392 


241 


876678 


184 


94I7I3 


425 


058287 


5o 


ii 


9 -8i8536 


240 


9.876568 


184 


9-941968 


425 


io-o58o32 


4o 


12 


818681 


240 


876457 


184 


942223 


425 


o57777 


48 


i3 


818825 


240 


876347 


184 


942478 


425 


057522 


47 


i4 


818969 


240 


876236 


i85 


942733 


425 


057267 


46 


i5 


819113 


240 


876125 


i85 


942988 


425 


057012 


45 


16 


819257 


240 


876014 


i85 


943243 


425 


056757 


44 


17 


819401 


240 


875904 


1 85 


9434Q8 


425 


o565o2 


43 


18 


819545 


239 


875793 


i85 


943752 


425 


o56248 


42 


19 


819689 


239 


875682 


i85 


944007 


425 


055993 


4i 


20 


819832 


239 


875571 


i85 


944262 


425 


o55738 


4o 


21 


9.819976 


239 


9-875459 


i85 


9-9445I7 


425 


io-o55483 


3 9 


22 


820120 


239 


875348 


i85 


944771 


424 


o55229 


38 


23 


820263 


239 


875237 


i85 


945026 


424 


054974 


37 


24 


820406 


23 9 


875126 


186 


94528l 


424 


054719 


36 


25 


82o55o 


238 


875014 


186 


945535 


424 


o5446o 


35 


26 


820693 


238 


874903 


186 


945790 


424 


o542io 


34 


27 


820836 


238 


874791 


186 


946o45 


424 


o53955 


33 


28 


820979 


238 


874680 


186 


946299 


424 


053701 


32 


29 


821122 


238 


874568 


186 


946554 


424 


o53446 


3i 


3o 


821265 


238 


874456 


186 


946808 


424 


o53i92 


3o 


3i 


9-821407 


238 


9.874344 


186 


9-947063 


424 


10-052937 


29 


32 


82i55o 


238 


874232 


187 


9473l8 


424 


052682 


28 


33 


821693 


23 7 


8741 2 I 


187 


947572 


424 


052428 


27 


34 


82i835 


237 


874009 


187 


947827 


424 


052173 


26 


35 


821977 


237 


873896 


187 


948081 


424 


051919 


25 


36 


822120 


237 


873784 


187 


948335 


424 


o5i665 


24 


37 


822262 


237 


873672 


187 


948590 


424 


o5i4io 


23 


38 


822404 


23 7 


873560 


187 


948844 


424 


o5n56 


22 


3 9 


822546 


237 


873448 


187 


949099 


424 


050901 


21 


4o 


822688 


236 


873335 


187 


949303 


424 


050647 


20 


4i 


9 .82283o 


236 


9.873223 


187 


9-949608 


424 


io-o5o392 


IQ 


42 


822972 


236 


873lIO 


188 


949862 


424 


o5oi38 


18 


43 


823n4 


236 


872998 


188 


95oil6 


424 


049884 


H 


44 


823255 


236 


872885 


188 


95o37l 


424 


049629 


16 


45 


823397 


236 


872772 


188 


95o625 


424 


049375 


i5 


46 


823539 


236 


872659 


188 


950879 


424 


0491 2 1 


14 


47 


823680 


235 


872547 


188 


961 i33 


424 


048867 


i3 


48 


823821 


235 


872434 


188 


9§i388 


424 


048612 


12 


49 


823963 


235 


872321 


188 


951642 


424 


o483 58 


11 


5o 


824104 


235 


872208 


188 


951896 


424 


048104 


10 


5i 


9.824245 


235 


9-872095 


189 


9-952i5o 


424 


10-047850 


n 


52 


824386 


235 


871981 


. 189 


9524o5 


424 


047595 


8 


53 


824527 


235 


871868 


189 


952659 


424 


047341 


7 


54 


824668 


234 


871755 


189 


952913 


424 


047087 


6 


55 


824808 


234 


871641 


189 


953167 


423 


046833 


5 


56 


824949 


234 


871528 


189 


953421 


423 


046579 


4 


57 


825090 


234 


87I4I4 


189 


953675 


423 


046323 


3 


58 


82523o 


234 


87I30I 


189 


953929 


423 


046071 


2 


5 9 


825371 


234 


87U87 


189 


954i83 


423 


045817 


1 


60 


8255n 


234 


87IO73 


190 


954437 


423 


045563 





/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


1 


13] 


L° 












i 


t8° 



60 


LOGARITHMIC SINES, 


TANGENTS, ETC 


Table II. 


42° 














137° 


r 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


1 





9.8255il 


234 


9-871073 


190 


9.954437 


423 


10-045563 


60 


i 


82565i 


233 


870960 


190 


954691 


423 


045309 


5 9 


2 


825791 


233 


870846 


190 


954946 


423 


o45o54 


58 


3 


825931 


233 


870732 


190 


955200 


423 


044800 


57 


4 


826071 


233 


870618 


190 


955454 


423 


044546 


56 


5 


826211 


233 


870504 


190 


955708 


423 


044292 


55 


6 


82635i 


233 


870390 


190 


955961 


423 


044039 


54 


7 


826491 


233 


870276 


190 


9562l5 


423 


043785 


53 


8 


82663i 


233 


870161 


190 


956469 


423 


o43 53 1 


52 


9 


826770 


232 


870047 


191 


956723 


423 


043277 


5i 


10 


826910 


232 


869933 


191 


956977 


423 


o43o23 


5o 


ii 


9-827049 


232 


9-869818 


191 


9-957231 


423 


10.042769 


49 


12 


827189 


232 


869704 


191 


957485 


423 


o425i5 


48 


i3 


827328 


232 


869589 


191 


957739 


423 


042261 


47 


U 


827467 


232 


869474 


191 


957993 


423 


042007 


46 


i5 


827606 


232 


86 9 36o 


191 


958247 


423 


041753 


45 


16 


827745 


232 


869245 


191 


9585oo 


423 


041600 


44 


17 


827884 


23l 


869130 


191 


958754 


423 


041246 


43 


18 


828023 


23l 


869015 


192 


959008 


423 


040992 


42 


*9 


828162 


23l 


868900 


192 


959262 


423 


040738 


4i 


20 


8283oi 


23l 


868785 


192 


959516 


423 


040484 


4o 


21 


9.828439 


23l 


9-868670 


192 


9.959769 


423 


io-o4o23i 


3 9 


22 


828378 


23l 


868555 


192 


960023 


423 


039977 


38 


23 


828716 


23 1 


868440 


192 


960277 


423 


039723 


37 


24 


828855 


23o 


868324 


192 


96o53o 


423 


039470 


36 


25 


828993 


23o 


868209 


192 


960784 


423 


039216 


35 


26 


829131 


23o 


868093 


192 


961038 


423 


038962 


34 


2"7 


829269 


23o 


867978 


i 9 3 


961292 


423 


o38io8 


33 


28 


829407 
829545 


23o 


867862 


i 9 3 


961545 


423 


o38455 


32 


29 


23o 


867747 


i 9 3 


961799 


423 


o382oi 


3i 


3o 


829683 


23o 


86 7 63 1 


i 9 3 


962052 


423 


037948 


3o 


3i 


9-829821 


229 


9.867515 


i 9 3 


9-962306 


423 


10-037694 


20 


32 


829959 


229 


86 7 3 99 


i 9 3 


962560 


423 


037440 


28 


33 


830097 


229 


867283 


i 9 3 


962813 


423 


037187 


27 


34 


83o2J4 


229 


867167 


i 9 3 


963067 


423 


036933 


26 


35 


83o372 


229 


86 7 o5i 


i 9 3 


963320 


423 


o3668o 


25 


36 


83o5o9 


229 


866 9 35 


194 


963574 


423 


036426 


24 


37 


83o646 


229 


866819 


i 9 4 


9 63828 


423 


036172 


23 


38 


830784 


229 


866703 


194 


964081 


423 


035919 


22 


3 9 


830921 


228 


866586 


194 


964335 


423 


035665 


21 


4o 


83io58 


228 


866470 


i 9 4 


9 64588 


422 


o354i2 


20 


4i 


q-83i io5 


228 


9-866353 


194 


9.964842 


422 


io-o35i58 


10 


42 


83i332 


228 


866237 


194 


965095 


422 


o349o5 


10 


43 


831469 


228 


866120 


194 


965349 


422 


o3465i 


17 


44 


83 1 606 


228 


866004 


i 9 5 


965602 


422 


034398 


16 


45 


83 1 742 


228 


865887 


i 9 5 


9 65855 


422 


o34U5 


i5 


46 


831879 


228 


865770 


i 9 5 


966109 


422 


033891 


14 


47 


832oi5 


227 


865653 


i 9 5 


966362 


422 


o33638 


i3 


48 


832i52 


227 


865536 


195 


966616 


422 


033384 


12 


49 


832288 


227 


865419 


i 9 5 


966869 


422 


o33i3i 


11 


5o 


832425 


227 


865302 


i 9 5 


96712J 


422 


032877 


10 


5i 


9-83256i 


227 


9-865i85 


i 9 5 


9.967376 


422 


10-032624 


Q 


52 


832697 


227 


865o68 


i 9 5 


967629 


422 


032371 


8 


53 


832833 


227 


864950 


i 9 5 


967883 


422 


032117 


7 


54 


832969 


226 


864833 


196 


9 68i36 


422 


o3i864 


6 


55 


833io5 


226 


864716 


196 


9 6838 9 


422 


o3i6u 


5 


56 


833241 


226 


864598 


196 


968643 


422 


o3i357 


4 


57 


833377 


226 


864481 


196 


968896 


422 


o3no4 


3 


58 


8335i2 


226 


864363 


196 


969149 


422 


o3o85i 


2 


5 9 


833648 


226 


864245 


196 


969403 


422 


030597 


1 


60 


833783 


226 


864127 


196 


969656 


422 


o3o344 





/ 


Cosine. 


D. 


Sine. 


D. 


' Cotang. 


D. 


Tang. 


r 


132 















470 





















Table II. LOGARITHMIC SINES, 


TANGENTS, ETC. 


61 


43 c 














136 a 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


1 





9-833783 


226 


9.864127 


196 


9-969656 


422 


lo-o3o344 


60 


i 


833919 


225 


864010 


196 


969909 


422 


030091 


5 9 


2 


834o54 


225 


8638 9 2 


197 


970162 


422 


029838 


58 


3 


834189 


225 


863774 


197 


970416 


422 


029584 


57 


4 


834325 


225 


863656 


197 


970669 


422 


029331 


56 


5 


83446o 


225 


863538 


197 


970922 


422 


029078 


55 


6 


834595 


225 


863419 


197 


971 175 


422 


028825 


54 


7 


83473o 


225 


8633oi 


197 


971429 


422 


028571 


53 


8 


834865 


225 


863 1 83 


197 


971682 


422 


0283i8 


52 


9 


834999 


224 


863o64 


197 


971935 


422 


028065 


5i 


10 


835i34 


224 


862946 


198 


972188 


422 


027812 


5o 


ii 


9-835269 
8354o3 


224 


9.862827 


198 


9-972441 


422 


10-027559 


49 


12 


224 


862709 


198 


972695 


422 


027300 


48 


i3 


835538 


224 


862590 


198 


972948 


422 


027052 


47 


14 


835672 


224 


862471 


198 


973201 


422 


026799 


46 


i5 


835807 


224 


862353 


198 


973454 


422 


026546 


45 


16 


835g4i 


224 


862234 


198 


973707 


422 


026293 


44 


\l 


836075 


223 


862115 


198 


973960 


422 


026040 


43 


8362o 9 


223 


861996 


198 


9742l3 


422 


025787 


42 


19 


836343 


223 


861877 


198 


974466 


422 


025534 


4i 


20 


836477 


223 


861758 


199 


974720 


422 


025280 


40 


21 


9-8366i 1 


223 


9 .86i638 


199 


9.974973 


422 


10-025027 


3 9 


22 


836745 


223 


86i5i 9 


199 


975226 


422 


024774 


38 


23 


836878 


223 


861400 


199 


975479 


422 


024521 


37 


24 


837012 


222 


861280 


199 


975732 


422 


024268 


36 


25 


837146 


222 


861161 


199 


975985 


422 


o24oi5 


35 


26 


837279 


222 


861041 


199 


976238 


422 


023762 


34 


27 


837412 


222 


860022 


199 


976491 


422 


023509 


33 


20 


837546 


222 


860002 


199 


976744 


422 


023256 


32 


29 


837679 


222 


860682 


200 


976997 


422 


o23oo3 


3i 


3o 


83 7 8i2 


222 


86o562 


200 


97725o 


422 


022750 


3o 


3i 


9.837945 


222 


9-860442 


200 


9-9775o3 


422 


10-022497 


29 


32 


838078 


221 


86o322 


200 


977756 


422 


022244 


28 


33 


8382U 


221 


860202 


200 


978009 


422 


021991 


27 


34 


838344 


221 


860082 


200 


978262 


422 


021738 


26 


35 


838477 


221 


859962 


200 


9785i5 


422 


021485 


25 


36 


8386io 


221 


85 9 842 


200 


978768 


422 


021232 


24 


12 


838742 


221 


85 97 2i 


201 


979021 


422 


020979 


23 


838875 


221 


859601 


201 


979274 


422 


020726 


22 


3 9 


839007 


221 


85 9 48o 


201 


979527 


422 


020473 


21 


40 


839140 


220 


85 9 36o 


201 


979780 


422 


020220 


20 


4i 


9.839272 


220 


9-859239 


201 


9-980033 


422 


10-019967 


IO 


42 


83o4o4 


220 


85oiiq 


201 


980286 


422 


OI97U 


10 


43 


83 9 536 


220 


858998 


201 


98o538 


422 


OI9462 


17 


44 


83 9 668 


220 


858877 


201 


980791 


421 


OI9209 


16 


45 


83 9 8oo 


220 


858756 


202 


981044 


421 


OI8956 


i5 


46 


839932 


220 


858635 


202 


981297 


421 


O18703 


14 


47 


840064 


219 


8585U 


202 


981560 


421 


Ol845o 


i3 


48 


840196 


219 


8583 9 3 


202 


981803 


421 


OI8197 


12 


49 


84o328 


219 


858272 


202 


982056 


421 


017944 


11 


5o 


840459 


219 


858i5i 


202 


982309 


421 


OI769I 


10 


5i 


9.840591 


219 


9-85802Q 


202 


9-982562 


421 


10-017438 





52 


840722 


219 


85 79 o8 


202 


982814 


421 


OI7186 


8 


53 


84o854 


219 


85 77 86 


202 


983067 


421 


010933 


7 


54 


840985 


219 


85 7 665 


203 


983320 


421 


Ol668o 


6 


55 


841 1 16 


2l8 


85 7 543 


203 


983573 


421 


OI6427 


5 


56 


841247 


2l8 


857422 


203 


983826 


421 


Ol6l74 


4 


n 


841378 


2l8 


857300 


203 


984079 


421 


Ol592I 


3 


841 509 


2l8 


85 7 i 7 8 


203 


984332 


421 


oi5668 


2 


5 9 


841640 


2l8 


85 7 o56 


203 


984584 


421 


oi54i6 


1 


60 


841771 


2l8 


856 9 34 


203 


984837 


421 


0i5i63 





/ 


Cosine. 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


t 


18£ 


,° 












4 


t6° 



62 


LOGARITHMIC SINES, 


TANGENTS, ETC 


Table II. 


44° 














135° 


/ 


Sine. 


D. 


Cosine. 


D. 


Tang. 


D. 


Cotang. 


1 





9-841771 


2l8 


9.856934 


203 


9-984837 


421 


IO«oi5i63 


60 


i 


841902 


2l8 


856812 


203 


985oyo 


421 


01 49 10 


5 9 


2 


842033 


218 


8566 9 o 


204 


q85343 


421 


014657 


58 


3 


842163 


217 


856568 


204 


985596 


421 


014404 


57 


4 


842294 


217 


856446 


204 


9 85848 


421 


0i4i52 


56 


5 


842424 


217 


856323 


204 


986101 


421 


013899 


55 


6 


842555 


217 


856201 


204 


986354 


421 


oi3646 


54 


I 


842685 


217 


856078 


204 


986607 


421 


oi3393 


53 


842815 


217 


855 9 56 


204 


986860 


421 


oi3i4o 


52 


9 


842946 


217 


855833 


204 


9871 12 


421 


012888 


5i 


10 


843076 


217 


855711 


205 


987365 


421 


012635 


5o 


ii 


9 '843206 


2l6 


9-855588 


205 


9.987618 


421 


10*012382 


^9 


12 


843336 


2l6 


855465 


205 


987871 


421 


012129 


48 


i3 


843466 


2l6 


855342 


205 


988123 


421 


011877 


47 


U 


8435 9 5 


2l6 


855219 


205 


988376 


421 


011624 


46 


i5 


843725 


216 


855o 9 6 


205 


988629 


421 


011371 


45 


16 


843855 


2l6 


854973 


205 


988882 


421 


011118 


44 


17 


843984 


2l6 


85485o 


205 


989134 


421 


010866 


43 


18 


8441 i4 


2l5 


854727 


206 


989387 


421 


oio6i3 


42 


*9 


844243 


2l5 


8546o3 


206 


989640 


421 


oio36o 


41 


20 


844372 


2l5 


85448o 


206 


989893 


421 


010107 


4o 


21 


9- 8445o2 


2l5 


9-854356 


206 


9.990145 


421 


10-009855 


3 9 


22 


84463i 


2l5 


854233 


206 


990398 


421 


009602 


38 


23 


844760 


2l5 


854109 


206 


990601 


421 


009349 


37 


24 


844889 


2l5 


853 9 86 


206 


990903 


421 


009097 


36 


25 


845oi8 


2l5 


853862 


206 


991 1 56 


421 


008844 


35 


26 


845i47 


2l5 


853738 


206 


991409 


421 


008591 


34 


11 


845276 


214 


8536i4 


207 


991662 


421 


oo8338 


33 


8454o5 


214 


853490 


207 


991914 


421 


008086 


32 


29 


845533 


214 


853366 


207 


992167 


421 


007833 


3i 


36 


845662 


214 


853242 


207 


992420 


421 


007080 


3o 


3i 


9*845790 


214 


9 -853ii8 


207 


9.992672 


421 


10-007328 


29 


32 


845919 


214 


852994 


207 


992925 


421 


007075 


28 


33 


846047 


214 


852869 


207 


993178 


421 


006822 


27 


34 


846175 ■ 


214 


852745 


207 


99343i 


421 


006569 


26 


35 


8463o4 


214 


852620 


207 


99 3683 


421 


006317 


25 


36 


846432 


2l3 


852496 


208 


993936 


421 


006064 


24 


37 


84656o 


2l3 


8523 7 i 


208 


994189 


421 


oo58n 


23 


38 


846688 


2l3 


852247 


208 


99444i 


421 


oo5559 


22 


3 9 


846816 


2l3 


852122 


208 


994694 


421 


oo53o6 


21 


4o 


846944 


2l3 


85 1 997 


208 


994947 


421 


oo5o53 


20 


4i 


9-847071 


2l3 


9-851872 


208 


9.995199 


421 


10.004801 


19 


42 


847199 


2l3 


851747 


208 


995452 


421 


004548 


18 


43 


847327 


2l3 


85i622 


208 


995705 


421 


004295 


17 


44 


847454 


212 


85i497 


209 


99 5 9 57 


421 


oo4o43 


16 


45 


847582 


212 


85i3 7 2 


209 


996210 


421 


003790 


i5 


46 


847709 


212 


85i246 


209 


996463 


421 


oo3537 


14 


47 


847836 


212 


85ii2i 


209 


996715 


421 


oo3285 


i3 


48 


847964 


212 


85oq 9 6 


209 


996968 


421 


oo3o32 


12 


49 


848091 


212 


850870 


209 


997221 


421 


002779 


11 


5o 


848218 


212 


85o745 


209 


997473 


421 


002627 


10 


5i 


9-848345 


212 


9-85o6io 


209 


9-997726 


421 


10-002274 





52 


848472 


211 


85o493 


210 


997979 


421 


002021 





53 


8485 99 


211 


85 368 


210 


998231 


421 


001769 


7 


54 


848726 


211 


85 242 


210 


998484 


421 


ooi5i6 


6 


55 


848852 


211 


85on6 


210 


998737 


421 


001263 


5 


56 


848979 


211 


849990 


210 


998989 


421 


OOIOII 


4 


5 7 


849106 


211 


849864 


210 


999242 


421 


000758 


3 


58 


849232 


211 


849738 


210 


999495 


421 


ooo5o5 


2 


5 9 


849359 


211 


8496 1 1 


210 


999747 


421 


ooo253 


1 


60 


849485 


211 


84g485 


210 


IO'OOOOOO 


421 


10-000000 





/ 


Cosine. 

i 


D. 


Sine. 


D. 


Cotang. 


D. 


Tang. 


1 


13 


1° 












45° 



TABLE III., 



OF 



NATURAL SINES AND TANGENTS; 



TO 



EVERY DEGKEE AND MINUTE OF THE QUADRANT. 



If the given angle is less than 45°, look for the degrees and the title of the 
column, at the top of the page ; and for the minutes on the left. But if the angle 
is "between 45° and 90 , look for the degrees and the title of the column, at the 
bottom / and for the minutes on the right. 

The Secants and Cosecants, which are not inserted in this table, may be easily 
supplied. If 1 be divided by the cosine of an arc, the quotient will be the secant 
of that arc. And if 1 be divided by the sine, the quotient will be the cosecant. 

The values of the Sines and Cosines are less than a unit, and are given in deci- 
mals, although the decimal point is not printed. So also, the tangents of arcs less 
than 45°, and cotangents of arcs greater than 45°, are less than a unit and are ex- 
pressed in decimals with the decimal point omitted. 



64 NATURAL SINES AND COSINES. Table III. 


/ 


0° 


1° 


2° 


3° 


4° 


1 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 





00000 


Unit. 


01745 


99985 


o3490 


99939 


o5234 


99 863 


06976 


99756 


60 


i 


00020 


Unit. 


OI774 


99984 


o35i9 


99938 


o5263 


99861 


07005 


99754 


5 9 


2 


ooo58 


Unit. 


oi8o3 


99984 


03548 


99937 


05292 


99860 


07034 


99752 


58 


3 


00087 


Unit. 


oi832 


99983 


03577 


99936 


o532i 


99 858 


07063 


99750 


5 7 


4 


00116 


Unit. 


01862 


99983 


o36o6 


99935 


o535o 


99857 


07092 


99748 


56 


5 


ooi45 


Unit. 


01891 


99982 


o3635 


99934 


05379 


99 855 


071 2 1 


99746 


55 


6 


00175 


Unit. 


01920 


99982 


o3664 


99933 


o54o8 


99854 


07150 


99744 


54 


7 


00204 


Unit. 


01949 


99981 


03693 


99932 


o5437 


99852 


07179 


99742 


53 


8 


00233 


Unit. 


01978 


9Q980 


o3723 


9 99 3 1 


o5466 


99851 


07208 


99740 


52 


9 


00262 


Unit. 


02007 


99980 


03752 


9993o 


o5495 


99849 


07237 


99738 


5i 


10 


00291 


Unit. 


o2o36 


99979 


03781 


99929 


o5524 


99847 


07266 


997 36 


5o 


ii 


00320 


99999 


02065 


99979 


o38io 


99927 


o5553 


99846 


07295 


99734 


49 


12 


oo34q 


99999 


02094 


99978 


o3839 


99926 


o5582 


99844 


07324 


99731 


48 


i3 


00378 


99999 


02123 


99977 


o3868 


99925 


o56n 


99842 


07353 


99729 


47 


U 


00407 


99999 


02l52 


99977 


03897 


99924 


o564o 


99841 


07382 


99727 


46 


i5 


oo436 


99999 


02181 


99976 


03926 


99923 


05669 


99839 


0741 1 


99725 


45 


16 


00465 


99999 


022II 


99976 


03955 


99922 


o56 9 8 


99 838 


07440 


99723 


44 


17 


00495 


99999 


02240 


99975 


o3 9 84 


99921 


05727 


99 836 


07469 


99721 


43 


10 


oo524 


99999 


02260 


99974 


o4oi3 


99919 


o5756 


99834 


07498 


997 1 9 


42 


19 


oo553 


99998 


02298 


99974 


04042 


99918 


05785 


99 833 


07527 


99716 


4i 


20 


oo582 


99998 


02327 


99973 


04071 


99917 


o58i4 


9983i 


07556 


997 1 4 


4o 


21 


0061 1 


99998 


02356 


99972 


04100 


99916 


o5844 


99829 


07585 


99712 


39 


22 


00640 


99998 


02385 


99972 


04129 


999 l5 


o58 7 3 


99827 


07614 


99710 


38 


23 


00669 


99998 


02414 


99971 


o4i5o 


999 l3 


05902 


99826 


07643 


99708 


37 


24 


00698 


99998 


02443 


99970 


04188 


99912 


05931 


99824 


07672 


99705 


36 


25 


00727 


99997 


02472 


99969 


04217 


9991 1 


05960 


99822 


07701 


99703 


35 


26 


00756 


99997 


02501 


99969 


04246 


99910 


05989 


99821 


07730 


99701 


34 


27 


00785 


99997 


o253o 


99968 


04275 


99909 


06018 


99819 


07739 


99699 


33 


20 


00814 


99997 


o256o 


99967 


o43 04 


99907 


06047 


99817 


07788 


99696 


32 


29 


00844 


99996 


02089 


99966 


04333 


99906 


06076 


99815 


07817 


99694 


3r 


3o 


00873 


99996 


02618 


99966 


04362 


99905 


o6io5 


99813 


07846 


99692 


3o 


3i 


00902 


99996 


02647 


99965 


04391 


99904 


06 1 34 


99812 


07875 


99689 


29 


32 


00931 


99996 


02676 


99964 


04420 


99902 


06 1 63 


99810 


07904 


99687 


28 


33 


00960 


99995 


02705 


99963 


04440 


99901 


06192 


99808 


07933 


99685 


27 


34 


00989 


99995 


02734 


99963 


o447» 


99900 


06221 


99806 


07962 


99 683 


26 


35 


01018 


99995 


02763 


99962 


04507 


99898 


o625o 


99804 


07991 


99680 


25 


36 


01047 


99995 


02792 


99961 


04536 


99897 


06279 


99803 


08020 


99678 


24 


37 


01076 


99994 


02821 


99960 


04565 


99896 


o63o8 


99801 


o8o4q 


99676 


23 


38 


ono5 


99994 


o285o 


99909 


04594 


99894 


o6337 


99799 


08078 


99673 


22 


3 9 


on34 


99994 


02879 


99959 


04623 


99893 


o6366 


99797 


08107 


99671 


21 


40 


01164 


99993 


02908 


99958 


04653 


99892 


06395 


99795 


08 1 36 


99668 


20 


4i 


01193 


99993 


02938 


99957 


04682 


99890 


06424 


99793 


o8i65 


99666 


19 


42 


01222 


99993 


02967 


99956 


047 1 1 


99889 


o6453 


99792 


08194 


99664 


l8 


43 


OI25l 


99992 


02996 


99955 


o474o 


99888 


06482 


99790 


08223 


99661 


17 


44 


01280 


99992 


o3o25 


99954 


04769 


99886 


o65n 


99788 


08252 


99659 


16 


45 


01309 


99991 


o3o54 


99953 


04798 


99885 


o654o 


99786 


08281 


99657 


i5 


46 


oi338 


99991 


o3o83 


99932 


04827 


99883 


06569 


99784 


o83io 


99654 


14 


47 


01367 


99991 


03ll2 


99952 


04856 


99882 


o65 9 8 


99782 


o833 9 


99652 


i3 


48 


01396 


99990 


o3i4i 


999 5 1 


04885 


99881 


06627 


99780 


o8368 


99649 


12 


P 


01425 


99990 


03170 


99930 


04914 


99879 


o6656 


99778 


08397 


99647 


11 


5o 


oi454 


99989 


03199 


99949 


04943 


99878 


o6685 


99776 


08426 


99644 


10 


5i 


oi483 


99989 


03220 


99948 


04972 


99876 


06714 


99774 


o8455 


99642 


9 


52 


oi5i3 


99989 


o3257 


99947 


o5ooi 


99875 


06743 


9977 2 


08484 


99639 


8 


53 | 01542 


99988 


o3286 


99946 


o5o3o 


99873 


06773 


99770 


o85i3 


99637 


7 


54 


01571 


99988 


o33i6 


99945 


o5o59 


99872 


06802 


99768 


08542 


99635 


6 


55 


01600 


99987 


o3345 


99944 


o5o88 


99870 


o683i 


99766 


08571 


99632 


5 


56 


01629 


99987 


03374 


99943 


05117 


99869 


06860 


99764 


08600 


99630 


4 


5 7 


oi658 


99986 


o34o3 


99942 


o5i46 


99867 


06889 


99762 


08629 


99627 


3 


58 


01687 


99986 


o3432 


99941 


o5i75 


99866 


06918 


99760 


o8658 


99626 


2 


59 


01716 


99985 


03461 


99940 


o52o5 


99864 


06947 


99758 


08687 


99622 


1 


60 


01745 


99985 


03490 


99939 


o5234 


99863 


06976 


99756 


08716 


99619 





/ 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


/ 


89° 


88° 


87° 


86° 


85° 



Table III. 


NATURAL SINES AND COSINES. 


65 


/ 


5 





6° 


1° 


8° 


9° 


1 

60 


Sine 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 





08716 


99619 


10453 


99452 


12187 


99255 


l 3 9H 


99027 


1 5643 


98769 


i 


08745 


99617 


10482 


99449 


I22l6 


9925l 


i3 9 46 


99023 


15672 


98764 


5 9 


2 


08774 


99614 


io5ii 


99446 


12245 


99248 


1397D 


99019 


1 5701 


98760 


58 


3 


o88o3 


99612 


10 54o 


99443 


12274 


99244 


14004 


990l5 


i573o 


98755 


57 


4 


o883i 


99609 


10569 


99440 


12302 


99240 


i4o33 


9901 1 


i5 7 58 


98751 


56 


5 


08860 


99607 


io5 97 


99437 


i233i 


99237 


1 406 1 


99006 


i5 7 8 7 


98746 


55 


6 


08889 


99604 


10626 


99434 


1 2~36o 


99233 


14090 


99002 


i58i6 


98741 


54 


7 


08918 


99602 


io655 


9943l 


i238 9 


99230 


14119 


98998 


1 5845 


98737 


53 


8 


08947 


99J99 


10684 


99428 


12418 


99226 


14148 


98994 


i58 7 3 


98732 


52 


9 


08976 


99596 


10713 


99424 


12447 


99222 


U177 


98990 


15902 


98728 


5i 8 


10 


09005 


99594 


10742 


99421 


12476 


99219 


14205 


98986 


i5 9 3i 


98723 


5o | 


ii 


09034 


99 5oi 


10771 


99418 


i25o4 


99213 


14234 


98982 


i5 9 5 9 


98718 


49 I 


12 


09063 


99588 


10800 


9941 5 


12533 


992 1 1 


14263 


98978 


i5 9 88 


987a 


48 1 


i3 


09092 


99586 


10829 


99412 


12562 


99208 


14292 


98973 


16017 


98709 


47 


14 


09121 


99583 


io858 


99409 


12591 


99204 


14320 


98969 


16046 


98704 


46 


i5 


09150 


99580 


10887 


99406 


12620 


99200 


14349 


98965 


16074 


98700 


45 


16 


09179 


9 9 5 7 8 


10916 


99402 


12649 


99197 


i43 7 8 


98961 


i6io3 


98695 


44 


17 


09208 


99 5 7 5 


10945 


99399 


12678 


99 I 9 3 


14407 


9 8 9 5 7 


i6i32 


98690 


43 


18 


09237 


99572 


10973 


99396 


12706 


99189 


14436 


98953 


16160 


98686 


42 


l 9 


09266 


99 5 7 o 


11002 


99393 


12735 


99186 


14464 


98948 


16189 


98681 


41 


20 


09295 


99067 


iio3i 


99390 


12764 


99182 


14493 


98944 


16218 


98676 


40 


21 


09324 


99564 


1 1060 


99 386 


12793 


99178 


14522 


98940 


16246 


98671 


39 


22 


09353 


99562 


1 1089 


99 383 


12822 


99175 


U55i 


98936 


16275 


98667 


38 


23 


09382 


99559 


11118 


99380 


i285i 


99171 


i458o 


98931 


1 63 04 


98662 


37 
36 


24 


0941 1 


99556 


1 1 147 


99 3 77 


12880 


99167 


14608 


98927 


16333 


9 865 7 


25 


09440 


99553 


1 1 176 


99374 


12908 


99163 


i463 7 


98923 


1 636 1 


9 8652 


35 


26 


09469 


9955i 


II205 


99370 


12937 


99160 


14666 


98919 


16390 


98648 


34 


27 


09498 


99548 


11234 


99367 


12966 


991 56 


14695 


989U 


1 641 9 


98643 


33 


28 


09527 


99545 


1 1 263 


99364 


12995 


99152 


14723 


98910 


16447 


9 8638 


32 


29 


09556 


99542 


11291 


99360 


i3o24 


99148 


14752 


98906 


16476 


9 8633 


3i 


3o 


09085 


99540 


Il320 


99 35 7 


i3o53 


99144 


14781 


98902 


i65o5 


98629 


3o 


3i 


09614 


99 53 7 


1 1349 


99354 


i3o8i 


99i4i 


14810 


98897 


16533 


98624 


29 


32 


09642 


99534 


11378 


9935i 


i3iio 


99i37 


14838 


98893 


i6562 


98619 


28 


33 


09671 


9953i 


1 1407 


99347 


i3i39 


g9i33 


14867 


98889 


16591 


98614 


27 


34 


09700 


99528 


1 1436 


99344 


i3i68 


99129 


14896 


98884 


16620 


98609 


26 


35 


09729 


99526 


1 1465 


99341 


i3i 9 7 


99125 


14925 


98880 


16648 


98604 


25 


36 


09758 


99523 


1 U94 


99337 


13226 


99122 


14954 


98876 


16677 


98600 


24 


37 


09787 


99520 


n523 


99334 


i3254 


99118 


14982 


98871 


16706 


9 85 9 5 


23 


38 


09816 


99517 


n552 


9933i 


i3283 


99H4 


i5oii 


98867 


16734 


98390 


22 


3 9 


09845 


995i4 


n58o 


99327 


i33i2 


99110 


i5o4o 


9 8863 


i6 7 63 


9 8585 


21 


4o 


09874 


995i 1 


1 1609 


69324 


i334i 


99106 


15069 


9 8858 


16792 


9 858o 


20 


4i 


09903 


99508 


u638 


99320 


13370 


99102 


1 5097 


9 8854 


16820 


985 7 5 


'8 


42 


09932 


99506 


1 1667 


99 3 1 7 


13399 


99098 


i5i26 


98849 


16849 


98570 


18 


43 


09961 


995o3 


1 1696 


993i4 


13427 


99094 


i5i55 


98845 


16878 


9 8565 


17 


44 


09990 


99500 


11725 


99310 


1 3456 


99001 


i5i84 


98841 


16906 


98561 


16 


45 


10019 


99497 


II754 


99307 


13485 


99087 


l52I2 


9 8836 


i6 9 35 


9 8556 


i5 


46 


10048 


99494 


1 1783 


993o3 


i35i4 


99083 


i524i 


9 8832 


16964 


9855i 


14 


47 


10077 


99491 


11812 


9g3oo 


1 3 543 


99079 


15270 


98827 


16992 


98546 


i3 


48 


10106 


99488 


1 1 840 


99297 


13572 


99075 


1 5299 


98823 


17021 


98541 


12 


49 


ioi35 


99485 


1 1869 


99293 


i36oo 


99071 


15327 


98818 


17050 


9 8536 


11 


5o 


10164 


99482 


1 1 898 


99290 


i362 9 


99067 


1 5356 


98814 


17078 


9 853i 


10 


5i 


10192 


99479 


11927 


99286 


i3658 


99063 


i5385 


98809 


17107 


9 8526 


9 


52 


10221 


99476 


11956 


99283 


13687 


99059 


1 54i4 


9 88o5 


17136 


98521 


8 


53 


10200 


99473 


1 1 985 


99279 


i3 7 i6 


99055 


1 5442 


98800 


17164 


9 85i6 


7 


54- 


10279 


99470 


12014 


99276 


13744 


99o5i 


1 547 1 


98796 


17193 


9 85u 


6 


55 


io3o8 


99467 


12043 


99272 


13773 


99047 


i55oo 


98791 


17222 


9 85o6 


5 


56 


io337 


99464 


12071 


99269 


i38o2 


99043 


15529 


98787 


17250 


985oi 


4 


5 7 


io366 


99461 


12100 


99263 


i383i 


99039 


i5557 


98782 


17279 


98496 


3 


58 


10395 


99458 


12120 


99262 


1 3 860 


99035 


1 5586 


98778 


17308 


98491 


2 


5 9 


10424 


99455 


I2l58 


99258 


i388 9 


9903 1 


i56i5 


98773 


17336 


98486 


1 


60 


10453 


99452 


12187 


99255 


13917 


99027 


1 5643 


98769 


17365 


98481 





/ 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


t 


84° 


83° 


82° 


81° 


80° 



66 




NATURAL SINES AND COSINES. Table III. 


i 


10° 


11° 


12° 


13° 


14° 


/ 
60 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 
20791 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 





17365 


98481 


1 908 1 


9 8l63 


97813 


r 
22495 | 97437 


24192 


97o3o 


i 


17393 


98476 


19100 


98137 


20820 


97809 


22523 97430 


24220 


97023 | 


5o 


2 


17422 


98471 


i 9 i38 


98l52 


20848 


97803 


22552 


97424 


24249 


97016 | 


58 


3 


I745l 


98466 


19167 


98146 


20877 


97797 


22580 


97417 


24277 


97008 j 


57 


4 


17479 


98461 


19193 


98140 


20905 


9779 1 


22608 


9741 1 


243o5 


97001 1 


56 


5 


17508 


98455 


19224 


98l35 


20933 


97784 


22637 


97404 


24333 


96994 j 


55 


6 


17537 


9845o 


19252 


98129 


20962 


97778 


2 2665 


97398 


24362 


96987 


54 


7 


17565 


98445 


19281 


98124 


20990 


97772 


22693 


973qi 


24390 


96980 


53 


8 


17394 


98440 


19309 


98118 


21019 


97766 


22722 


97384 


24418 


96973 j 52 


9 


17623 


98435 


i 9 338 


98112 


21047 


97760 


22750 


97 3 7 8 


24446 


96966 1 5 1 


10 


i 7 65i 


9843o 


i 9 366 


98107 


21076 


977 5 4 


22778 


97371 


24474 


96959 5o 


ii 


17680 


98425 


19395 


98101 


21 104 


97748 


22807 


97365 


245o3 


96962 4o 


12 


17708 


98420 


19423 


98096 


2Il32 


97742 


22835 


97358 


2453i 


96946 48 


i3 


17737 


98414 


19452 


98090 


2Il6l 


97733 


22863 


9735i 


24559 


9 6 9 3 7 47 


U 


17766 


98409 


1 948 1 


98084 


21 189 


97729 


22892 


97345 


24387 


96930 1 46 


i5 


17794 


98404 


19309 


98079 


2I2l8 


97723 


22920 


97338 


246i5 


96923 45 


16 


17823 


98399 


i 9 538 


98073 


21246 


97717 


22948 


9733i 


24644 


96916 


44 


17 


17852 


98394 


19366 


98067 


21275 


97711 


22977 


97325 


24672 


96909 


43 


18 


17880 


98389 


i 9 3 9 5 


98061 


2i3o3 


97703 


23oo5 


973i8 


24700 


96902 


42 


19 


17909 


9 8383 


19623 


98o56 


2i33i 


97698 


23o33 


97311 


24728 


96894 


4i 


20 


17937 


98378 


19652 


98030 


2i36o 


97692 


23o62 


973o4 


24756 


96887 


40 


21 


17966 


98373 


19680 


98044 


2i388 


97686 


23090 


97298 


24784 


96880 


39 


22 


17995 


9 8368 


19709 


98039 


21417 


97680 


23u8 


97201 


248i3 


96873 


38 


23 


18023 


9 8362 


19737 


9 8o33 


21445 


97673 


23 1 46 


97284 


24841 


96866 


37 


24 


18002 


98357 


19766 


98027 


21474 


97667 


23i75 


97278 


24869 


96868 


36 


25 


1 808 1 


98352 


19794 


98021 


2l5o2 


97661 


23203 


97271 


24897 


96861 


35 


26 


18109 


98347 


19823 


98016 


2i53o 


97655 


2323l 


97264 


24925 


96844 


34 


27 


i8i38 98341 


19801 


98010 


21559 


97648 


23260 


97257 


24934 


96837 


33 


28 


18166 98336 


19880 


98004 


21587 


97642 


23288 


97251 


24982 


96829 


32 


29 


18193 98331 


19908 


97998 


21616 


97636 


233i6 


97244 


25oio 


96822 


3i 


3o 


18224 


98323 


19937 


97992 


21644 


97630 


23345 


97237 


25o38 


9 68i5 


3o 


3i 


18252 


98320 


19965 


97987 


21672 


97623 


23373 


9723o 


25o66 


96807 


29 


32 


18281 


983 1 5 


19994 


97981 


21701 


97617 


23401 


97223 


25094 


96800 


28 


33 


i83o 9 


983io 


20022 


97975 


21729 


97611 


23429 


97217 


25l22 


96793 


27 


34 


i8338 


983o4 


20o5l 


97969 


21758 


97604 


23458 


97210 


23l5l 


96786 


26 


35 


i836 7 


98299 


20079 


97 9 63 


21786 


97598 


23486 


97203 


26179 


96778 


25 


36 


i83 9 5 


98294 


20108 


97938 


21814 


97392 


235i4 


97196 


26207 


96771 


24 


37 


18424 


98288 


; 2oi36 


979 32 


21843 


97585 


23542 


97189 


25235 


96764 


23 


38 


18452 


98283 


2oi65 


97946 


21871 


97579 


23571 


97182 


25263 


96766 


22 


3 9 


1 848 1 


98277 


20193 


97940 


21899 


97573 


23599 


97176 


26291 


96749 


21 


4o 


18509 


98272 


20222 


979 3 4 


21928 


97566 


23627 


97169 


25320 


96742 


20 


4i 


i8538 


98267 


20230 


97928 


21956 


97560 


23656 


97162 


25348 


96734 


IO 


42 


18667 


98261 


20279 


97922 


21985 


97553 


23684 


97i55 


25376 


96727 


IO 


43 


18593 


98256 


20307 


97916 


220l3 


97547 


23712 


97148 


25404 


96719 


17 


44 


18624 


98250 


2o336 


97910 


22041 


97541 


23740 


97141 


25432 


96712 


16 


45 


i8652 i 9824D 


20364 


97903 


22070 


97534 


23769 


97134 


25460 


96705 


i5 


46 


1 868 1 


98240 


20393 


97899 


22098 


97528 


23797 


97127 


25488 


96697 


14 


47 


18710 


98234 


20421 


97893 


22126 


97521 


23825 


97120 


255i6 


96690 


i3 


48 


18738 


98229 


20430 


97887 


22l55 


973i5 


23853 


97ii3 


25545 


96682 


12 


49 


18767 


98223 


20478 


97881 


22183 


97508 


23882 


97106 


26673 


96676 


11 


5o 


18795 


98218 


20307 


97875 


22212 


97302 


23910 


97100 


26601 


96667 


10 


5i 


18824 


98212 


2o535 


97869 


22240 


97496 


23 9 38 


97093 


26629 


96660 


9 


52 


18862 


98207 


20563 


97863 


22268 


97489 


23966 


97086 


25657 


96663 


8 


53 


18881 


98201 


20392 


97837 


22297 


97483 


23995 


97079 


25685 


96645 


7 


54 


18910 


98196 


20620 


9785i 


22325 


97476 


24023 


97072 


26713 


9 6638 


6 


55 


i8 9 38 


98190 


20649 


97845 


22353 


97470 


24o5i 


97065 


25741 


96630 


5 


56 


18967 


98185 


20677 


97839 


22382 


97463 


24079 


97058 


25769 


96623 


4 


5 7 


18990 


98179 


20706 


97833 


22410 


97457 


24108 


97o5i 


26798 


96615 


3 


58 


19024 


98174 


20734 


97827 


22438 


9745o 


24i36 


97044 


25826 


96608 


2 


5 9 


19002 


98168 


20763 


97821 


22467 


97444 


24164 


97037 


25854 


96600 


1 


60 


19081 


98163 


20791 


97815 


22495 


97437 


24192 


97o3o 


25882 


96693 





/ 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


/ 


79° 


78° 


77° 


76° 


75° 



Table III. NATURAL SINES AND COSINES. 67 


/ 


15° 


16° 


17° 


18° 


19° 


t 


Sine. 1 Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 





25882 


96593 


27564 J 96126 


29237 


9563o 


30902 


95io6 


32557 


94552 


60 


i 


25910 


96585 


27592 j 961 18 


29265 


95622 


30929 


95097 


32584 


94542 


59 


2 


2D 9 38 


96578 


27620 


96110 


29293 


956i3 


30957 


9 5o88 


326l2 


94533 


58 


3 


2D966 


96570 


27648 


96102 


29321 


956o5 


30985 


95079 


32639 


94523 


57 


4 


20994 


96562 


27676 


96094 


29348 


95596 


3J0I2 


95070 


32667 


945l4 


56 


5 


26022 


96555 


27704 


96086 


29376 


9 5588 


3 1 040 


95061 


32694 


945o4 


55 


6 


260DO 


96547 


27731 


96078 


29404 


95579 


3 1 068 


95o52 


32722 


94495 


54 


7 


26079 


96540 


27759 


96070 


29432 


95571 


31095 


95o43 


32749 


94485 


53 


8 


26107 


96532 


27787 


96062 


29460 


95562 


3ii23 


95o33 


32777 


94476 


52 


9 


26i35 


96524 


2 7 8l5 


96054 


29487 


95554 


3ii5i 


95024 


32804 94466 


5i 


10 


26163 


96517 


27843 


96046 


295l5 


95545 


3n 7 8 


95oi5 


32832 


94457 


5o 


ii 


26191 


96509 


27871 


96037 


29543 


95536 


3i2o6 


95oo6 


3285 9 


94447 


4q 


12 


26219 


96502 


27899 


96029 


29571 


9 5528 


3i233 


94997 


32887 


9 4438 


48 


i3 


26247 


96494 


27927 


96021 


29599 


95519 


3i26i 


94988 


32914 


94428 


47 


14 


26275 


96486 


27955 


96013 


29626 


955i 1 


3i28 9 


94979 


32942 


94418 


46 


ID 


263o3 


96479 


.27983 


96005 


29654 


955o2 


3i3i6 


94970 


32969 


94409 


45 


16 


2633i 


96471 


2801 1 


95997 


29682 


95493 


3i344 


94961 


32997 


94399 


44 


n 


26359 


96463 


28039 


95989 


29710 


95485 


3i372 


94952 


33o24 


94390 


43 


18 


26387 


96456 


28067 


95981 


29737 


95476 


3 1 399 


94943 


33o5i 


9438o 


42 


*9 


26415 


96448 


28095 


95972 


29765 


95467 


31427 


94933 


33079 


94370 


4i 


20 


26443 


96440 


28123 


95964 


29793 


954D9 


3 1 454 


94924 


33io6 


9436i 


40 


21 


26471 


96433 


28i5o 


95g56 


29821 


9545o 


31482 


94915 


33i34 


943 5 1 


39 


22 


265oo 


96425 


28178 


9D948 


29849 


9544i 


3i5io 


94906 


33 1 61 


94342 


38 


23 


26528 


96417 


28206 


9D940 


29876 


95433 


3i53 7 


94897 


33i8 9 


94332 


37 


24 


26556 


96410 


28234 


95931 


29904 


95424 


3 1 565 


94888 


332i6 


94322 


36 


2D 


26584 


96402 


28262 


9D923 


29932 


954i5 


31D93 


94878 


33244 


943 1 3 


35 


26 


26612 


96394 


28290 


95915 


29960 


95407 


31620 


94869 


33271 


943o3 


34 


27 


26640 


9 6386 


283i8 


95907 


29987 


9 53o8 


31648 


94860 


33298 


94293 


33 


28 


26668 


96379 


28346 


95898 


3ooi 5 


95389 


3i6 7 5 


9 485 1 


33326 


94284 


32 


29 


26696 


96371 


28374 


95890 


3oo43 


9538o 


3 1 703 


94842 


33353 


94274 


3i 


3o 


26724 


9 6363 


28402 


95882 


30071 


95372 


3i73o 


9 4832 


3338i 


94264 


3o 


3i 


26752 


9 6355 


28429 


95874 


30098 


9 5363 


3i 7 58 


94823 


334o8 


94254 


29 


32 


26780 


96347 


28457 


9 5865 


3oi26 


95354 


31786 


94814 


33436 


94245 


28 


33 


26808 


96340 


28485 


95857 


3oi54 


95345 


3i8i3 


948o5 


33463 


94235 


27 


34 


26836 


96332 


285i3 


95849 


3oi82 


95337 


3i84i 


9479 s 


33490 94225 


26 


35 


26864 


96324 


28541 


95841 


30209 


95328 


3 1 868 


94786 


335i8 


942 ID 


25 


36 


26892 


96316 


2856 9 


9583*2 


30237 


95319 


3i8 9 6 


94777 


33545 


94206 24 


3 7 


26920 


9 63o8 


28597 


95824 


3o265 


953io 


31923 


94768 


33573 


94196 


23 


38 


26948 


9b3oi 


28625 


9 58i6 


30292 


953oi 


3i95i 


94758 


336oo 


94186 


22 


3 9 


26976 


96293 


28652 


95807 


3o32o 


952o3 


31979 


94749 


33627 


94176 


21 


4o 


27004 


96285 


28680 


9D799 


3 0348 


95284 


32006 


94740 


33655 


94167 


20 


4i 


27032 


96277 


28708 


9D791 


30376 


95275 


32034 


9473o 


33682 


94l57 


19 


42 


27060 


96269 


28 7 36 


9D782 


3o4o3 


95266 


32061 


94721 


33710 


94147 


l8 


43 


27088 


96261 


28764 


95774 


3 o43 1 


95257 


32089 


94712 


33737 


9 4l37 


17 


44 


27116 


96253 


28792 


95766 


3o459 95248 


32ii6 


94702 


33764 


94127 


16 


45 


27144 


96246 


28820 


9 5 7 5 7 


3o486 


90240 


32144 


94693 


33792 


941 1 8 


i5 


46 


27172 


96238 


28847 


95749 


3o5i4 


9323l 


32171 


94684 


338i 9 


94108 


14 


47 


27200 


96230 


28875 


9D740 


3o542 


95222 


32199 


94674 


33846 


94098 


i3 


48 


27228 


96222 


28903 


95732 


3o57o 


9D2l3 


32227 


94665 


338 7 4 94088 


12 


49 


27206 


96214 


28931 


92724 


30597 


95204 


32254 


94656 


33901 


94078 


11 


5o 


27284 


96206 


28909 


95715 


3o625 


95195 


32282 


94646 


33929 


94068 j 10 


5l 


27312 


96198 


28987 


95707 


3o653 


95186 


32309 


94637 


33 9 56 


94o58 


9 


52 


27340 


96190 


29015 


90698 


3o68o 


95177 


32337 


94627 


33983 94049 


8 


53 


27368 


96182 


29042 


9D690 


30708 


95168 


32364 


94618 


34oi 1 


94039 


7 


54 


27396 


96174 


29070 


9568i 


3o736 


95159 


32392 


94609 


34o38 


94029 


6 


55 


27424 


96166 


29098 


95673 


30763 


95i5o 


32419 


94599 


34o65 


94019 5 


56 


27452 


9 6i58 


29126 


95664 


3o7qi 


95142 


32447 94590 


34093 


94009 


4 


57 


27480 | 


96i5o | 


29154 


95656 


30819 


9Di33 


32474 9458o 


34120 


93999 


3 


58 27508 ! 


96142 1 


29182 


95647 


30846 


95124 


325o2 94571 


34i47 


93989 


2 


59 j 27536 1 


96134 


29209 


95639 


30874 


9D1 15 


32529 94561 


34h5 


93979 | 1 


60 ! 27564 1 96126 


29237 


9563o 


30902 


95io6 


32557 1 94552 


34202 


93969 

1 


, 1 


Cosine, j Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


1 
Sine. 


/ 


/ 


74° 


73° 


72° 


71° 


7C 


|° 



68 NATURAL SINES AND COSINES. Table III. [ 





20° 


21° 


22° 


23° 


24° 


1 
t '■ 


Sine. Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 
92718 


Sine. 


Cosine. 


Sine. 


Cosine. 


34202 


93969 


3583 7 


9 3358 


3746l 


39073 


92o5o 


40674 


9l355 


60 - 


i 


34229 


93959 


35864 


93348 


37488 


92707 


39IOO 


92o3o 


40700 


9l343 


5 9 . 


2 


34257 


93949 


358 9 i 


93337 


375i5 


92697 


39127 


92028 


40727 


9l33l 


58 


3 


34284 


93939 


35918 


93327 


37542 


92686 


39l53 


92016 


40753 


91319 


57 


4 


343 1 1 


9 3 9 2 9 


35945 


933i6 


37569 


92675 


39180 


92005 


40780 


91307 


56 


5 


34339 


93919 


35973 


933o6 


37595 


92664 


39207 


91994 


40806 


9I2o5 


55 ' 


6 


34366 


93909 


36ooo 


93295 


37622 


92653 


39234 


91982 


4o833 


91283 


54 


7 


34393 


93899 


36027 


9 3285 


37649 


92642 


39260 


91971 


40860 


91272 


53 


8 


34421 


93889 


36o54 


93274 


37676 


9263l 


39287 


9l 9 5o 


40886 


91260 


52 


9 


34448 


93879 


36o8i 


93264 


37703 


92620 


393l4 


91948 


40913 


91248 


5i 


IO 


34475 


93869 


36io8 


93253 


37730 


92609 


39341 


91936 


40939 


91236 


5o 


ii 


345o3 


9385 9 


36i35 


93243 


37757 


92598 


39367 


91925 


40966 


91224 


49 ' 


12 


3453o 


93849 


36i62 


93232 


37784 


92587 


39394 


91914 


40992 


91212 


48 : 


i3 


34557 


9383 9 


36190 


93222 


37811 


92576 


39421 


91902 


41019 
4io45 


91200 


47 


i4 


34584 


93829 


36217 


93211 


37838 


92565 


39448 


91891 


91188 


46 


i5 


34612 


93819 


36244 


93201 


3 7 865 


92554 


39474 


91879 


41072 


91176 


45 


16 


34639 


93809 


36271 


93190 


37892 


92543 


395oi 


91868 


41098 


91 164 


44 


17 


34666 


93799 


36298 


93180 


37919 


92532 


3 9 528 


9 i856 


4ii25 


91 152 


43 


18 


34694 


93789 


36325 


93169 


37946 


92521 


3 9 555 


91845 


4n5i 


91 140 


42 


*9 


34721 


93779 


36352 


93159 


37973 


925io 


3 9 58i 


9 i833 


41178 


91128 


4i 


20 


34748 


93769 


363 79 


93148 


37999 


92499 


39608 


91822 


41204 


91116 


40 


21 


34775 


93759 


364o6 


93137 


38026 


92488 


3 9 635 


91810 


4i23i 


91104 


3 9 


22 


348o3 


93748 


36434 


93127 


38o53 


92477 


39661 


91799 


41257 


91092 


38 


23 


3483o 


93738 


3646i 


93i 16 


38o8o 


92466 


3 9 688 


91787 
91775 


41284 


91000 


37 


24 


34857 


93728 


36488 


93106 


38107 


92455 


39715 


4i3io 


91068 


36 


25 


34884 


93718 


365 1 5 


93095 


38i34 


92444 


39741 


91764 


4i337 


9io56 


35 


26 


34912 


93708 


36542 


93084 


38i6i 


92432 


39768 


91752 


4i363 


91044 


34 


2 1 


34939 


9 36 9 8 


3656 9 


93o74 


38i88 


92421 


3 9 7 9 5 


91741 


41390 


91032 


33 


28 


34966 


o3688 


365 9 6 


93o63 


382i5 


92410 


39822 


91729 


41416 


91020 


32 


29 


34993 


93677 


36623 


93o52 


38241 


92399 


39848 


91718 


41443 


91008 


3i 


3o 


35o2i 


93667 


3665o 


93042 


38268 


92388 


39875 


91706 


4U69 


90996 


3o 


3i 


35o48 


93657 


36677 


93o3i 


382 9 5 


92377 


39902 


91694 


4U96 


90984 


29 


32 


35o75 


93647 


36704 


93020 


38322 


92366 


39928 


91683 


4l522 


90972 


28 


33 


35io2 


93637 


36731 


93oio 


38349 


92355 


39955 


91671 


41549 


90960 


27 


34 


35i3o 


93626 


36 7 58 


92999 


38376 


92343 


39982 


91660 


4i5 7 5 


90948 


26 


35 


35i5 7 


93616 


36785 


92988 


384o3 


92332 


40008 


91648 


41602 


90936 


25 


36 


35i84 


93606 


368i2 


92978 


3843o 


92321 


4oo35 


9 1 636 


41628 


90924 


24 


37 


352i 1 


93596 


3683o 


92967 


38456 


923io 


40062 


91625 


4i655 


9091 1 


23 


38 


35239 


9 3585 


36867 


92956 


38483 


92299 


40088 


91613 


41681 


90899 


22 


3 9 


35266 


93575 


368 9 4 


92945 


385io 


92287 


401 1 5 


91601 


41707 


90887 


21 


4o 


35293 


9 3565 


36921 


92935 


38537 


92276 


40141 


91590 


41734 


90875 


20 


4i 


3532o 


9 3555 


36 9 48 


92924 


38564 


92265 


40168 


9 i5 7 8 


41760 


90863 


IQ 


.42 


35347 


93544 


36975 


92913 


38591 


92254 


40195 


9 1 566 


41787 


9085 1 


18 


43 


35375 


93534 


37002 


92902 


386i 7 


92243 


40221 


9 i555 


4i8i3 


90839 


17 


44 


35402 


93524 


37029 


92892 


38644 


9223i 


40248 


9i543 


41840 


90826 


16 

15 


45 


35429 


935i4 


37056 


92881 


386 7 i 


92220 


40275 


9i53i 


41866 


90814 


46 


35456 


935o3 


37083 


92870 


386 9 8 


92209 


4o3oi 


9i5io 


41892 


90802 1 14 


47 


35484 


93493 


37110 


92859 


38 7 25 


92198 


4o328 


9i5o8 


41919 


90790 


i3 


48 


355n 


9 3483 


37137 


92849 


38 7 52 


92186 


4o355 


9U96 


41945 


90778 


12 


49 


35538 


93472 


37164 


9 2838 


38 77 8 


92175 


4o38i 


91484 


41972 


90766 


11 


5o 


35565 


93462 


37191 


92827 


388o5 


92164 


40408 


9U72 


41998 


90753 


10 


5i 


35592 


93452 


37218 


92816 


38832 


92l52 


4o434 


91 46 1 


42024 


90741 


9 


52 


35619 


93441 


37245 


92805 


3885 9 


92141 


40461 


91449 


42o5i 


90729 


8 


53 


35647 


9343i 


37272 


92794 


38886 


92i3o 


40488 


91437 


42077 


90717 


7 


54 


35674 


93420 


37299 


92784 


38 9 i2 


92119 


4o5i4 


91425 


42104 


90704 


6 


55 


35701 


93410 


37326 


92773 


38 9 3 9 


92107 


4o54i 


9UU 


42i3o 


90692 


5 


56 


35728 


98400 


37353 


92762 


38 9 66 


92096 


40567 


91402 


42 1 56 


90680 


4 


5 7 


35755 


93389 


3738o 


92751 


38 99 3 


92085 


40594 


91390 


42 1 83 


90668 


3 


58 


35782 


93379 


37407 


92740 


39020 1 92073 


40621 


9 i3 7 8 


42209 
42235 


9o655 


2 


5 9 


358io 


93368 


37434 


92729 


39046 


92062 


40647 


9i366 


90643 


1 


60 


35837 


93358 


37461 


92718 


39073 


92o5o 


40674 


9i355 


42262 


9063 1 





s 
5 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 

• 


Cosine. 


Sine. 


Cosine. 


Sine. 


/ i 


69° 


68° 


67° 


66° 


65° 



; Table III NATURAL SINES AND COSINES. 69 


/ 


25° 


26° 


27° 


28° 


29° 


/ 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 





42202 


9063 1 


43837 


89879 


45399 


89101 


46947 


88295 


48481 


87462 


60 


i 


42288 


90618 


43863 


89867 


45425 


89087 


46973 


88281 


485o6 


87448 


5 9 


2 


423i5 


90606 


4388 9 


89854 


4545l 


89074 


46999 


88267 


48532 


87434 


58 


3 


42341 


90594 


43916 


89841 


45477 


89061 


47024 


88254 


48557 


87420 


57 


4 


42367 


go582 


43942 


89828 


455o3 


89048 


47o5o 


88240 


48583 


87406 


56 


5 


423 9 4 


90569 


43 9 68 


89816 


45529 


8 9 o35 


47076 


88226 


48608 


87391 


55 


6 


42420 


90557 


43994 


89803 


45554 


89021 


47 1 01 


88213 


48634 


87377 


54 


1 7 


42446 


90545 


44020 


89790 


4558o 


89008 


47127 


88199 


48659 


87363 


53 


8 


42473 


90532 


44046 


89777 


456o6 


88 99 5 


47i53 


88i85 


48684 


87349 


52 


9 


42499 


90520 


44072 


89764 


45632 


88981 


47178 


88172 


48710 


87335 


5i 


10 


42525 


90507 


44098 


89752 


45658 


8S968 


47204 


88i58 


48735 


8 7 32l 


5o 


ii 


42552 


90495 


44124 


89739 


45684 


88 9 55 


47229 


88144 


48761 


8 7 3o6 


49 


12 


42578 


90483 


44i 5 1 


89726 


45710 


88942 


47255 


88i3o 


48786 


87292 


48 


i3 


42604 


90470 


44177 


89713 


45736 


88928 


47281 


88117 


488 1 1 


87278 


47 


14 


4263i 


90458 


44203 


89700 


45762 


88 9 i5 


473o6 


88io3 


48837 


87264 


46 


i5 


42657 


90446 


44229 


89687 


45787 


88902 


47332 


88089 


48862 


87250 


45 


' 16 


42683 


90433 


44255 


89674 


458i3 


88888 


47358 


88075 


48888 


87235 


44 


i 17 


42709 


90421 


44281 


89662 


45839 


88870 


47383 


88062 


48913 


87221 


43 


• 18 


42736 


90408 


44307 


89649 


45860 


88862 


47409 


88048 


48 9 38 


87207 


42 


»9 


42762 


90306 


44333 


8 9 636 


45891 


88848 


47434 


88o34 


48964 


87193 


4i 


20 


42788 


9o383 


44359 


89623 


45917 


88835 


47460 


88020 


48989 


87178 


4o 


21 


428i5 


90371 


44385 


89610 


45942 


88822 


47486 


88006 


49014 


87164 


3 9 


22 


42841 


9o358 


444i 1 


89597 


45 9 68 


88808 


475i 1 


87993 


49040 


87150 


38 


23 


42867 


90346 


44437 


8 9 584 


45994 


88795 


47537 


87979 
8 79 65 


49065 


■87136 


37 


24 


42894 


9o334 


44464 


89571 


46020 


88782 


47562 


49090 


87121 


36 


25 


42920 


90321 


44490 


8 9 558 


46046 


88768 


47588 


8 79 5 1 


49116 


87107 


35 


26 


42946 


90309 


445 1 6 


89545 


46072 


88755 


47614 


87937 


49 1 4i 


87093 


34 


! 27 


42972 


90296 


44542 


8 9 532 


46097 


88741 


47639 


87923 


49166 


87079 


33 


• 28 


42999 


90284 


44568 


89519 


46i23 


88728 


47660 


87909 


49192 


87064 


32 


| 29 


43o25 


90271 


44594 


89506 


46U9 


88 7 i5 


47690 


87896 


49217 


87050 


3i 


3o 


43o5i 


90269 


44620 


89493 


46175 


88701 


477 l6 


87882 


49242 


87036 


3o 


3i 


43077 


90246 


44646 


89480 


46201 


88688 


47741 


87868 


49268 


87021 


29 


32 


43 1 04 


90233 


44672 


89467 


46226 


88674 


47767 


87854 


49293 


87007 


28 


33 


43i3o 


90221 


44698 


89454 


46252 


88661 


47793 


87840 


49318 


86 99 3 


27 


34 


43 1 56 


90208 


44724 


89441 


46278 


88647 


47818 


87826 


49344 


86978 


26 


35 


43i82 


90196 


4475o 


89428 


463 04 


88634 


47844 


87812 


49369 


86964 


25 


36 


43209 


90183 


44776 


8g4i5 


4633o 


88620 


47869 


87798 


49394 


86949 


24 


37 


43235 


90171 


44802 


89402 


46355 


88607 


47895 


87784 


49419 


86 9 33 


23 


38 


4326i 


901 58 


44828 


8 9 38 9 


4638 1 


885 9 3 


47920 


87770 


49445 


86921 


22 


3 9 


43287 


90146 


44854 


89376 


46407 


8858o 


47946 


87756 


49470 


86906 


21 


4o 


433 1 3 


90i33 


44880 


8 9 363 


46433 


88566 


47971 


87743 


49495 


86892 


20 


4i 


43340 


90120 


44906 


8 9 35o 


46458 


88553 


47997 


87729 


49521 


86878 


IQ 


42 


43366 


90108 


44932 


89337 


46484 


8853 9 


48022 


8 77 i5 


49546 


86863 


ID 


43 


43392 


90095 


44958 


8 9 324 


465 10 


88526 


48048 


87701 


49571 


86849 


17 


44 


434i8 


90082 


44984 


8 9 3n 


46536 


885i2 


48073 


87687 


49596 


86834 


16 


45 


43445 


90070 


45oio 


89298 


4656 1 


88499 


48099 


87673 


49622 


86820 


i5 


46 


43471 


90057 


45o36 


89285 


46587 


88485 


48124 


87659 


49647 


868o5 


14 


47 


43497 


90045 


45o62 


89272 


466 1 3 


88472 


481 5o 


87645 


49672 


86791 


i3 


48 


43523 


90032 


45o88 


89259 


4663 9 


88458 


48175 


87631 


49697 


86777 


12 


49 


43549 


90019 


45u4 


89245 


46664 


88445 


48201 


87617 


49723 


86762 


11 


5o 


43575 


90007 


45 1 40 


89232 


46690 


8843i 


48226 


8 7 6o3 


49748 


86748 


10 


5i 


436o2 


89994 


45 1 66 


89219 


46716 


88417 


48252 


8 7 58o 


49773 


86 7 33 


9 


. 52 


43628 


89981 


45192 


89206 


46742 


88404 


48277 


87575 


49798 


86719 


8 


53 


43654 


80968 


452i8 


8 9 io3 


46767 


883 9 o 


483o3 


87561 


49824 


86704 


7 


• 54 


4368o 8 99 56 


45243 


89180 


46793 


88377 


48328 


87546 


49849 


86690 


6 


" 55 


43706 


89943 


45269 


89167 


46819 


88363 


48354 


8753-2 


49874 


86675 


5 


56 


43733 


89930 


45296 


891 53 


46844 


88349 


483 7 o 


8 7 5i8 


49899 


86661 


4 


i 5 7 


43759 


89918 


45321 


89140 


46870 


88336 


484o5 


87504 


49924 


86646 


3 


; 58 


43785 


89905 


45347 


89127 


46896 


88322 


4843o 


87490 


49950 


86632 


2 


. 5 9 


438 1 1 


89892 


45373 


89114 


46921 


883o8 


48456 


87476 


49975 


86617 


1 


; 60 43837 


89879 


45399 


89101 


46947 


88295 


48481 


87462 


5oooo 


866o3 





4 7 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


r 


64° 


63° 


62° 


61° 


6( 


D° 





'70 NATURAL SINES AND COSINES: Table III. j 


! 

r ' 



30° 


81° 


32° 


33° 


34° 





Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


1 
Sine. 


Cosine. 


Sine. 


Cosine. 


5oooo 


866o3 


5i5o4 


85717 


52992 


848o5 


54464 


83867 


55919 


82^04 ! 60 


\ I 


5oo25 


86588 


5i529 


85702 


53oi7 


84789 


54488 


8385i 


55943 


82887 ! 59 


1- 2 


5oo5o 


86573 


5i554 


85687 


53o4i 


84774 


545 1 3 


83835 


55 9 68 


82871 | 58 


;. 3 


50076 


8655 9 


51579 


80672 


53o66 


84739 


54537 


838io 


50992 


82855 57 


• 4 


5oioi 


86544 


5 1604 


85657 


53091 


84743 


5456i 


838o4 


56oi6 82839 56 


5 


5oi26 


8653o 


51628 


85642 


53n5 


84728 


54586 


83 7 88 


56o4o ; 82822 55 


6 


5oi5i 


865i5 


5i653 


85627 


53 1 40 


84712 


54610 


83 77 2 


56o64 82806! 54 


7 


50176 


865oi 


5i6 7 8 


856i2 


53 1 64 


84697 


54635 


83756 


56o88 : 82790 53 


I 8 


50201 


86486 


5i7o3 


855 9 7 


53 1 89 


84681 


54659 


83740 


56ii2 i 82773 


52 


9 


50227 86471 


51728 


85582 


53214 


84666 


54683 


83 7 24 


56i36 82757 


5i 


10 


50252 


86457 


5i 7 53 


85567 


53238 


8465o 


54708 


83 7 o8 


56i6o , 82741 


5o 


\ ii 


50277 


86442 


51778 


8555i 


53263 


84635 


54732 83692 


56i84 j 82724 


4o 


12 


5o3o2 


86427 


5i8o3 


85536 


53288 


84619 


54756 836 7 6 


56208 82708 


48 


i3 


5o327 


864 1 3 


51828 


85521 


533i2 


84604 


54781 


8366o 


56232 


82692 


47 


U 


5o3o2 


863 9 8 


5i852 


855o6 


53337 


84588 


548o5 


83645 


56256 


82675 


46 


' i5 


5o377 


86384 


51877 


85491 


5336i 


84073 


54829 


8362 9 


56280 


82659 


45 


. 16 


5 040 3 


8636 9 


51902 


85476 


53386 


84557 


54854 


836i3 


563o5 


82643 44 


I n 


50428 


86354 


51927 


8546i 


534i 1 


84542 


54878 


83597 


56329 


82626 43 


: 18 


5o453 


8634o 


51932 


85446 


53435 


84526 


54902 


8358i 


56353 82610 


42 


i 19 


50478 


86325 


51977 


8543 1 


5346o 


845i 1 


54927 


83565 


563 7 7 


82593 


41 


' 20 


5o5o3 


863 10 


52002 


854i6 


53484 


84495 


54951 


83549 


564oi 


82577 


40 


j 21 


5o528 


86295 


52026 


854oi 


535o9 


84480 


54975 


83533 


56425 


8256i 


39 


22 


5o553 


86281 


D205l 


85385 


53534 


84464 


54999 


835i 7 


56449 


82544 


38 


23 


50578 


86266 


52076 


85370 


53558 


84448 


55o24 


835oi 


56473 


82528 


37 


: 24 


5o6o3 


86201 


52IOI 


85355 


53583 


84433 


55o48 


83485 


56497 


825u 


36 


25 


50628 


86237 


52126 


8534o 


53607 


84417 


55072 


8346 9 


56521 


82495 


35 


26 


5o654 


86222 


52i5i 


85325 


53632 


84402 


55097 


83453 


56545 


82478 


34 


: 27 


50679 


86207 


52175 


853io 


53656 


84386 


55i2i 


8343 7 


56569 


82462 


33 


.28 


50704 


86192 


52200 


85294 


5368i 


84370 


55 1 45 


83421 


565 9 3 


82446 


32 


. 2Q 


50729 


86178 


52225 


85279 


537o5 


84355 


55169 


834o5 


566i 7 


82429 


3i 


;3o 


50754 


86 1 63 


52250 


85264 


5373o 


84339 


55194 


8338 9 


06641 


824i3 


3o 


[3i 


50779 


86148 


52275 


85249 


53754 


84324 


552i8 


833 7 3 


56665 


82396 


2 9 


32 


5o8o4 


86i33 


52299 


85234 


53779 


843o8 


55242 


83356 


5668 9 


8238o 


28 


"33 


50829 


86119 


52324 


852i8 


538o4 


84292 


55 2 66 


83340 


56 7 i3 


82363 


27 


.34 


5o854 


86104 


52349 


852o3 


53828 


84277 


55291 


83324 


56 7 36 


82347 


26 


.35 


50879 


86089 


52374 


85 1 88 


53853 


84261 


553i5 


833o8 


56i6o 


8233o 25 


i 36 


50904 


86074 


52399 


85173 


53877 


84245 


5533 9 


832 9 2 


56 7 84 


823i4 


24 


;37 


50929 


86059 


52423 


85i5 7 


53902 


8423o 


55363 


832 7 6 


568o8 


82297 


23 


38 


50954 


86o45 


52448 


85i42 


53926 


84214 


55388 


8326o 


56832 


82281 


22 


: 3 9 


5o 979 


86o3o 


52473 


85127 


53g5i 


84198 


55412 


83244 


56856 


82264 


21 


i 40 


5 1 004 


86oi5 


52498 


85ii2 


53975 


84182 


55436 


83228 


5688o 


82248 


20 


S 4-1 


51029 


86000 


52522 


85o 9 6 


54ooo 


84167 


55460 


83212 


56904 


82231 


19 


42 


5io54 


85 9 85 


52547 


85o8i 


54024 


841 5 1 


55484 


83i 9 5 


56928 


82214 


18 


43 


51079 


85970 


52572 


85o66 


54049 


84i35 


555o9 


83 1 79 


56952 


82198 


17 


•44 


5uo4 


85956 


52597 


85o5i 


54073 


84120 


55533 


83 1 63 


56976 


82181 


16 


U5 


51129 


85941 


52621 


85o35 


54097 


84104 


55557 


83i4 7 


57000 


82i65 


i5 


46 


5ii54 


85 9 26 


52646 


85o2o 


54122 


84088 


5558i 


83i3i 


57024 


82148 


14 


■47 


5ii 79 


8591 1 


52671 


85oo5 


54146 


84072 


556o5 


83ii5 


57047 


82132 


i3 


48 


5i2o4 


858 9 6 


52696 


84989 


54171 


84057 


5563o 


83o 9 8 


57071 


82ii5 


12 


49 


51229 


8588i 


52720 


84974 


54195 


84041 


55654 


83o82 


57095 


82098 


11 


5o 


5i254 


85866 


52745 


84959 


54220 


84025 


55678 


83o66 


57119 


82082 


10 


i5i 


51279 


8585i 


52770 


84943 


54244 


84009 


55702 


83o5o 


57143 


82065 


9 


1 52 


5i3o4 


85836 


52794 


84928 


54269 


83994 


55726 


83o34 


57167 


82048 


8 


1 53 


5l32Q 


85821 


52819 


84913 


54293 


83978 


55750 


83oi7 


57191 


82032 


7 


54 


5i354 


858o6 


52844 


84897 


543i7 


83 9 62 


5577D 


83ooi 


57215 


82oi5 


6 


55 


51379 


85792 


52869 


84882 


54342 


83 9 46 


55 799 


82985 


5 7 238 


81999 


5 


:56 


5 1 404 


85777 


52893 


84866 


54366 


83 9 3o 


55823 


82969 


57262 


81982 


4 


57 


51429 


85762 


52918 


8485 1 


54391 


83915 


55847 


82953 


57286 


81965 


3 


58 


5 1 454 


85 7 47 


52943 


84836 


544i 5 


838 99 


55871 


82 9 36 


57310 


81949 


2 


59 ! 5i479 


85732 


52967 


84820 


54440 


83883 


558 9 5 


82920 


57334 


8i 9 32 


1 


60 


5i5o4 


83717 


52992 


848o5 


54464 


83867 


55919 


82904 


57358 


81915 





i 
j ' 

\i 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


1 


59° 


58° 


57° 


56° 


55° 



Table III. NATURAL SINES AND COSINES. 71 


i 




35° 


36° 


37° 


38° 


39° 


t 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


57358 


8101O 


58779 


80902 


60182 


79864 


6i566 


78801 


62932 


77715 


60 


i 


5 7 38i 


81899 


588o2 


8o885 


6o2o5 


79846 


6i58 9 


78783 


62955 


77696 


5 9 


i 


57405 


81882 


58826 


80867 


60228 


79829 


61612 


78765 


62977 


77678 


58 


3 


57429 


8i865 


58849 


8o85o 


6o25i 


79811 


6i635 


78747 


63ooo 


77660 


5 7 


4 


07453 


81848 


588 7 3 


8o833 


60274 


79793 


6i658 


78729 


63022 


77°4l 


56 


5 


57477 


8i832 


588 9 6 


80816 


60298 


79776 


61681 


78711 


63o45 


77623 


55 


6 


57501 


8i8i5 


58920 


80799 


6o32i 


797 58 


61704 


78694 


63o68 


77606 


54 


7 


57524 


81798 


58943 


80782 


6o344 


79741 


61726 


78676 


63090 


7 7 586 


53 


8 


57548 


81782 


58967 


80765 


60367 


79723 


61749 


78668 


63n3 


77568 


52 


9 


57572 


8i 7 65 


58990 


80748 


60390 


79706 


61772 


78640 


63i35 


77660 


5i 


10 


57596 


81748 


59014 


80730 


60414 


79688 


61795 


78622 


63 1 58 


7753i 


5o 


ii 


57619 


81731 


59037 


8o 7 i3 


60437 


79671 


61818 


78604 


63 1 80 


775i3 


49 


12 


57643 


817U 


59061 


80696 


60460 


79653 


61841 


78586 


632o3 


77494 


48 


i3 


57667 


81698 


59084 


80679 


6o483 


79635 


61864 


7 8568 


63225 


77476 


47 


U 


57691 


81681 


59108 


80662 


6o5o6 


79618 


61887 


7855o 


63248 


77458 


46 


i5 


57715 


81664 


59131 


80644 


60629 


79600 


61909 


78532 


63271 


77439 


45 


16 


5 77 38 


81647 


59164 


80627 


6o553 


79 583 


61932 


78614 


63293 


77421 


44 


n 


57762 


8i63i 


59178 


80610 


60676 


79565 


61955 


78496 


633i6 


77402 


43 


18 


57786 


81614 


59201 


80593 


60699 


79347 


61978 


78478 


63338 


77384 


42 


J 9 


5 7 8io 


8i5 97 


59225 


80576 


60622 


7953o 


62001 


78460 


6336i 


77366 


4i 


20 


5 7 833 


8i58o 


59248 


8o558 


6o645 


79512 


62024 


78442 


63383 


77347 


4o 


21 


57857 


8i563 


59272 


8o54i 


60668 


79494 


62046 


78424 


634o6 


77329 


3 9 


22 


5 7 88i 


81546 


69295 


8o524 


60691 


79477 


62069 


784o5 


63428 


77310 


38 


23 


57904 


8i53o 


5 9 3i8 


80507 


60714 


79459 


62092 


78387 


6345 1 


77292 


37 


24 


57928 


8i5i3 


59342 


80489 


6o 7 38 


79441 


62ii5 


78369 


63473 


77273 


36 


25 


57952 


81496 


59365 


80472 


60761 


79424 


62i38 


7835i 


63496 


77266 


35 


26 


57976 


81479 


5 9 38g 


8o455 


60784 


79406 


62160 


7 8333 


635i8 


77236 


34 


27 


57999 


81462 


59412 


8o43 8 


60807 


7 9 388 


62183 


7 83i5 


6354o 


77218 


33 


28 


58o23 


8i445 


5 9 436 


80420 


6o83o 


79371 


62206 


78297 


63563 


77199 


32 


2 9 


58047 


81428 


59459 


8o4o3 


6o853 


79353 


62229 


78279 


63585 


77181 


3i 


3o 


58070 


81412 


59482 


8o386 


60876 


79335 


6225l 


78261 


636o8 


77162 


3o 


3i 


58094 


8i3 9 5 


59606 


8o368 


60899 


79318 


62274 


78243 


6363o 


77144 


29 


32 


58n8 


81378 


59529 


8o35i 


60922 


79300 


62297 


78225 


63653 


77126 


28 


33 


58i4i 


8i36i 


59552 


8o334 


60945 


79282 


62320 


78206 


636 7 5 


77107 


27 


34 


58i6» 


81 344 


59576 


8o3i6 


60968 


79264 


62342 


78188 


636 9 8 


77088 


26 


35 


58i8 9 


8i32 7 


59699 


80299 


60991 


79247 


62365 


78170 


63720 


77070 


25 


36 


58212 


8i3io 


59622 


80282 


6ioi5 


79229 


62388 


78152 


63742 


77061 


24 


37 


58236 


8i2 9 3 


59646 


80264 


6io38 


79211 


6241 1 


78134 


63765 


77o33 


23 


38 


58260 


81276 


59669 


80247 


61061 


79193 


62433 


78116 


63787 


77014 


22 


3 9 


58283 


8i25 9 


59693 


8o23o 


61084 


79176 


62406 


78098 


638io 


76996 


21 


4o 


58307 


81242 


59716 


80212 


61107 


7 9 i58 


62479 


78079 


63832 


76977 


20 


41 


5833o 


81225 


59730 
59763 


80195 


6n3o 


79140 


62602 


78061 


63854 


76969 


19 


42 


58354 


81208 


80178 


6u53 


79122 


62624 


78043 


63877 


76940 


10 


43 


58378 


81191 


59786 


80160 


61176 


79105 


62547 


78026 


638 99 


76921 


17 


44 


584oi 


81174 


59809 


8oi43 


61199 


79087 


62570 


78007 


63922 


76903 


16 


45 


58425 


81167 


5 9 832 


8oi25 


61222 


79069 


62692 


77988 


63944 


76884 


i5 


46 


58449 


81140 


59856 


80108 


6i245 


79061 


62615 


77970 


63 9 66 


76866 


i4 


47 


58472 


81123 


59879 


80091 


61268 


79o33 


62638 


779 D 2 


63 9 8 9 


76847 


i3 


48 


58496 


81106 


59902 


80073 


61291 


79016 


62660 


77934 


6401 1 


76828 


12 


49 


585i9 


81089 


59926 


8oo56 


6i3i4 


78998 


62683 


77916 


64o33 


76810 


11 


5o 


58543 


81072 


59949 


8oo38 


6i337 


78980 


62706 


77897 


640 56 


76791 


10 


5i 


58567 


8io55 


59972 


80021 


6i36o 


78962 


62728 


77879 


64078 


76772 


9 


52 


58590 


8io38 


59995 


8ooo3 


6i383 


78944 


62761 


77861 


64100 


76754 


8 


53 


586 1 4 


81 02 1 


60019 


79986 


61406 


78926 


62774 


77843 


64123 


76735 


7 


54 


58637 


81004 


60042 


79968 


61429 


78908 


62796 


77824 


64i45 


76717 


6 


55 


5866i 


80987 


6oo65 


79901 


6i45i 


78891 


62819 


77806 


64167 


76698 


5 


56 


58684 


80970 


60089 


79934 


6i474 


78873 


62842 


77788 


64190 


76679 


4 


5 7 


58708 


80953 


60112 


79016 


61497 


78855 


62864 


77769 


64212 


76661 


3 


58 


58 7 3i 


8o 9 36 


6oi35 


79899 


6i52o 


78837 


62887 


77751 


64234 


76642 


2 


5 9 


58755 


80919 


6oi58 


79881 


6 1 543 


78819 


62909 


77733 


64256 


76623 


1. 


60 


58779 


80902 


60182 


79864 


6 1 566 


78801 


62932 


77715 


64279 


76604 





/ 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


1 


54° 


53° 


52° 


51° 


50° 



72 NATURAL SINES AND COSINES. Table III. 


/ 


40° 


41° 


42° 


43° 


44° 


/ 


Sine. 


Cosine. 


Sine. 1 Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


o 


64279 


76604 


656o6 


754]i 


66913 


743 1 4 


68200 


73i35 


69466 


71934 


60 


i 


643oi 


76586 


65628 


75452 


66 9 35 


74295 


68221 


73116 


69487 


71914 


5 9 


2 


64323 


76567 


6565o 


75433 


66 9 56 


74276 
74256 


68242 


73096 


69508 


71894 


58 


3 


64346 


76548 


65672 


754U 


66978 


68264 


73076 


69529 


71873 


57 


4 


64368 


7653o 


65694 


75395 


66999 


74237 


68285 


73o56 


69549 


71853 


56 


5 


64390 


765n 


65716 


7 53 7 5 


67021 


74217 


683o6 


73o36 


69570 


71833 


55 


6 


64412 


76492 


65738 


7 5356 


67043 


74198 


68327 


73oi6 


69091 


7l8l3 


54 


7 


64435 


76473 


65759 


75337 


67064 


74178 


68349 


72996 


69612 


71792 


53 


8 


64457 


76455 


65781 


7 53i8 


67086 


74i59 


68370 


72976 


6 9 633 


71772 


52 


9 


64479 


76436 


658o3 


75299 


67107 


74i39 


683 9 i 


72957 


69654 


71752 


5i 


10 


645oi 


76417 


65825 


73280 


67129 


74120 


68412 


72937 


69676 


71732 


5o 


ii 


64024 


76398 


65847 


75261 


67i5l 


74100 


68434 


72917 


69696 


71711 


49 


12 


64546 


7638o 


6586 9 


75241 


67172 


74080 


68455 


72897 


69717 


71691 


48 


i3 


64568 


7636 1 


658 9 i 


75222 


67194 


74061 


68476 


72877 


69737 


71671 


47 


U 


64590 


76342 


65913 


75203 


67215 


74041 


68497 


72857 


69758 


7i65o 


46 


i5 


64612 


76323 


65 9 35 


75i84 


67237 


74022 


685i8 


72837 


69779 


7i63o 


45 


16 


64635 


763o4 


65g56 


7 5i65 


6 7 258 


74002 


6853 9 


72817 


69800 


71610 


44 


17 


64657 


76286 


65978 


75146 


67280 


73 9 83 


6856i 


72797 


69821 


7i5 9 o 


43 


18 


64679 


76267 


66000 


75126 


67301 


73963 


68582 


72777 


69842 


71569 


42 


x 9 


64701 


76248 


66022 


75107 


6 7 323 


73944 


686o3 


72757 


69862 


7i549 


4i 


20 


64723 


76229 


66044 


75o88 


67344 


73924 


68624 


72737 


6 9 883 


71529 


4o 


21 


64746 


76210 


66066 


75069 


6 7 366 


73904 


68645 


72717 


69904 


7i5o8 


39 


22 


64768 


76192 


66088 


75o5o 


67387 


7 3885 


68666 


72697 


69925 


71488 


38 


23 


64790 


76173 


66109 


75o3o 


67409 


73865 


68688 


72677 


69946 


71468 


37 


24 


64812 


76154 


66i3i 


75on 


67430 


73846 


68709 


72657 


69966 


71447 


36 


25 


64834 


76i35 


66 1 53 


74992 


67452 


73826 


68730 


72637 


69987 


71427 


35 


26 


64856 


76116 


66175 


74973 


67473 


73806 


68751 


72617 


70008 


7U07 


34 


27 


64878 


76097 


66197 


74953 


67495 


73787 


68772 


72597 


70029 


7i386 


33 


2b 


64901 


76078 


66218 


74934 


6 7 5i6 


73767 


68 79 3 


72577 


70049 


7 1 366 


32 


29 


64923 


76059 


66240 


74915 


6 7 538 


73747 


68814 


72557 


70070 


7i345 


3i 


3o 


64945 


76041 


66262 


74896 


67559 


73728 


68835 


72537 


70091 


7i325 


3o 


3i 


64967 


76022 


66284 


74876 


67580 


73708 


68857 


72517 


70II2 


7i3o5 


29 


32 


64989 


76003 


663o6 


7485 7 


67602 


73688 


68878 


72497 


70l32 


71284 


28 


33 


65ou 


75984 


66327 


74838 


67623 


73669 


688 99 


72477 


70l53 


71264 


27 


34 


65o33 


75965 


66349 


74818 


67645 


73649 


68920 


72457 


70174 


71243 


26 


35 


65o55 


75946 


663 7 i 


74799 


67666 


73629 


68941 


72437 


70190 


•71223 


25 


36 


65077 


75927 


663 9 3 


74780 


67688 


73610 


68962 


72417 


70215 


71203 


24 


ll 


65 1 00 


75908 


664U 


74760 


67709 


73590 


68 9 83 


72397 


70236 


71182 


23 


65l22 


75889 


66436 


74741 


67730 


73570 


69004 


72377 


70257 


71162 


22 


3 9 


65 1 44 


75870 


66458 


74722 


67752 


7355i 


69026 


72357 


70277 


71141 


21 


4o 


65 1 66 


7585i 


66480 


747o3 


67773 


7353i 


69046 


72337 


70298 


71121 


20 


4i 


65 1 88 


75832 


665oi 


74683 


67795 


735 1 1 


69067 


72317 


70319 


71 100 


I? 


42 


652io 


758i3 


66523 


74664 


67816 


73491 


69088 


72297 


70339 


71080 


18 


43 


65232 


75794 


66545 


74644 


67837 


73472 


69109 


72277 


7o36o 


71059 


l l 


44 


65254 


75775 


66566 


74625 


67859 


73452 


69130 


72257 


7o38i 


7io3 9 


16 


45 


65276 


75756 


66588 


74606 


67880 


73432 


69151 


72236 


70401 


71019 


i5 


46 


652 9 8 


75 7 38 


66610 


74586 


67901 


734i3 


69172 


72216 


70422 


70998 


14 


47 


6532o 


75719 


66632 


74567 


67923 


73393 


69193 


72196 


70443 


70978 


i3 


48 


65342 


75700 


66653 


74548 


67944 


73373 


69214 


72176 


70463 


70957 


12 


i 9 


65364 


7568o 


66675 


74528 


67965 


73353 


69235 


72i56 


70484 


70937 


11 


5o 


65386 


7566i 


66697 


745o9 


67987 


73333 


69256 


72136 


7o5o5 


70916 


10 


5i 


654o8 


75642 


66718 


74489 


68008 


733i4 


69277 


72116 


7o525 


70896 


9 


52 


6543o 


75623 


66740 


74470 


68029 


73294 


69298 


72095 


70546 


70875 


8 


53 


65452 


75604 


66762 


7445 1 


68o5i 


73274 


69319 


72075 


70567 


7o855 


7 


54 


65474 


75585 


66783 


7443 1 


68072 


73254 


69340 


72o55 


70587 


70834 


6 


55 


65496 


75566 


668o5 


744i2 


68o 9 3 


73234 


69361 


72o35 


70608 


7 o8i3 


5 


56 


655i8 


75547 


66827 


74392 


68n5 


732i5 


69382 


72oi5 


70628 


70793 


4 


5 7 


6554o 


75528 


66848 


74373 


68i36 


73195 


69403 


71995 


70649 


70772 


3 


58 


65562 


75509 


66870 


74353 


68157 


73175 


69424 


71974 


70670 


70752 


2 


5 9 


65584 


75490 


66891 


74334 


68179 


7 3i55 


69445 


71954 


70690 


70731 


1 


60 


656o6 


75471 


66913 


743 1 4 


68200 


7 3i35 


69466 


71934 


7071 1 


7071 1 





/ 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


/ 


49° 


48° 


47 


46° 


45° 



Table III. NATURAL TANGENTS AND COTANGENTS. 73 


/ 


0° 


1° 


2° 




!° 


r 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 





00000 


Infinite. 


01746 


57-2900 


o3492 


28-6363 


o524i 


19.0811 


60 


i 


00029 


3437-75 


01775 


56 


35o6 


o352i 


28 


•3994 


05270 


10 


•9755 


5 9 


2 


ooo58 


1718-87 


01804 


55 


44i 5 


o355o 


28 


•1664 


05299 


18 


•8711 


58 


3 


00087 


II45-92 


oi833 


54 


56i3 


03579 


27 


•9372 


05328 


18 


.7678 


57 


4 


001 16 


85q 


•436 


01862 


53 


7086 


03609 


27 


.7117 


05357 


18 


-6656 


56 


5 


OOI45 


687 


•549 


01891 


52 


8821 


03638 


27 


.4899 


05387 


18 


•5645 


55 


6 


00175 


572 


•957 


01920 


52 


0807 


03667 


27 


•27l5 


o54i6 


18 


•4645 


54 


7 


00204 


491 


■ 106 


01949 


5i 


3o32 


03696 


27 


-o566 


o5445 


18 


• 3655 


53 


8 


00233 


429 


•718 


01978 


5o 


5485 


o3725 


26 


•845o 


o5474 


18 


•2677 


52 


9 


00262 


38i 


•971 


02007 


49 


8157 


03754 


26 


■636 7 


o55o3 


18 


• 1708 


5i 


10 


00291 


343 


•774 
•521 


02o36 


49 


1039 


03783 


26 


43 16 


o5533 


18 


•0750 


5o 


ii 


00320 


3l2 


02066 


48 


4121 


o38i2 


26 


•2296 


o5562 


*7 


• 9802 


49 


12 


oo349 


286 


•478 


02095 


47 


7395 


o3842 


26 


0307 


05591 


17 


• 8863 


48 


i3 


00378 


264 


•441 


02124 


47 


o853 


03871 


25 


8348 


o562o 


17 


• 79 34 


47 


14 


00407 


245 


• 552 


02i53 


46 


4489 


03900 


25 


6418 


o564q 


n 


• 7015 


46 


i5 


oo436 


229 


.182 


02182 


45 


8294 


03929 


25 


45i7 


05678 


17 


• 6106 


45 


16 


00465 


214 


•858 


02211 


45 


2261 


o3 9 58 


25 


2644 


05708 


n 


• 52o5 


44 


n 


00495 


202 


'219 


02240 


44 


6386 


03987 


25 


0798 


05737 


17 


•43 14 


43 


18 


oo524 


190 


.984 


02269 


44 


0661 


04016 


24 


8978 


05766 


n 


3432 


42 


19 


oo553 


180 


• 9 32 


02298 


43 


5o8i 


04046 


24 


7i85 


05795 


*7 


2558 


4i 


20 


oo582 


171 


-885 


02328 


42 


9641 


04075 


24 


54i8 


o5824 


17 


1693 


40 


21 


0061 1 


1 63 


•700 


02357 


42 


4335 


04104 


24 


3675 


o5854 


17 


0837 


3 9 


22 


00640 


1 56 


•259 


02386 


41 


•9 1 58 


o4i33 


24 


1957 


o5883 


16 


9990 


38 


23 


00669 


149 


•465 


024i5 


41 


4106 


04162 


24 


0263 


05912 


16 


9i5o 


37 


24 


00698 


143 


•237 


02444 


40 


9H4 


04191 


23 


85 9 3 


05941 


16 


83i 9 


36 


25 


00727 


i3 7 


•5o7 


02473 


4o 


4358 


04220 


23 


6945 


05970 


16 


7496 


35 


26 


00756 


l32 


•219 


02502 


3 9 


9 655 


o425o 


23 


532i 


05999 


16 


6681 


34 


27 


00785 


127 


•321 


0253i 


3 9 


5o59 


04279 


23 


3 7 i8 


06029 


16 


5874 


33 


28 


00814 


122 


•774 


o256o 


3 9 


o568 


o43 08 


23 


2137 


o6o58 


16 


5075 


32 


29 


00844 


118 


•54o 


02589 


38 


6177 


04337 


23 


0577 


06087 


16 


4283 


3i 


3o 


00873 


114 


•58 9 


02619 


38 


i885 


04366 


22 


9o38 


06116 


16 


3499 


3o 


3i 


00902 


no 


•892 


02648 


37 


7686 


04395 


22 


75i 9 


o6i45 


16 


2722 


29 


32 


00931 


,107 


• 426 


02677 


37 


35 79 


04424 


22 


6020 


06175 


16 


1952 


28 


33 


00960 


104 


•171 


02706 


36 


956o 


04454 


22 


454i 


06204 


16 


1 190 


27 


34 


00989 


101 


• 107 


02735 


36 


5627 


04483 


22 


3o8i 


o6233 


16 


0435 


26 


35 


01018 


98. 


2179 


02764 


36 


1776 


o45 1 2 


22 


1640 


06262 


i5 


9687 


25 


36 


01047 


9**" 


48 9 5 


02793 


35- 


8006 


o454i 


22 


0217 


06291 


i5 


8945 


24 


37 


01076 


92- 


908D 


02822 


35- 


43i3 


04570 


21 


88i3 


o632i 


i5 


8211 


23 


38 


ono5 


90- 


4633 


0285i 


35- 


0695 


04599 


21 


7426 


o635o 


i5 


7483 


22 


3 9 


ou35 


88- 


1436 


02881 


34- 


71D1 


04628 


21 


6o56 


06379 


i5 


6762 


21 


4o 


01 164 


85- 


o3 9 8 


02910 


34- 


3678 


04658 


21 


4704 


06408 


i5 


6048 


20 


4i 


01193 


83- 


8435 


02939 


34- 


0273 


04687 


21 


336 9 


06437 


i5 


534o 


IO 


42 


01222 


81 • 


8470 


02968 


33- 


6 9 35 


04716 


21 


2049 


06467 


i5 


4638 


l8 


43 


OI25l 


79- 


9434 


02997 


33- 


3662 


04745 


21 


0747 


06496 


i5 


3943 


17 


44 


01280 


78- 


1263 


o3o26 


33- 


0452 


04774 


20 


9460 


o6525 


i5 


3254 


16 


45 


01309 


76. 


3900 


o3o55 


32- 


73o3 


o48o3 


20 


8188 


o6554 


i5 


2571 


i5 


46 


oi338 


74- 


7292 


o3o84 


32- 


42i3 


o4832 


20 


6932 


o6584 


i5 


i8 9 3 


14 


47 


01367 


7 3- 


1390 


o3u4 


32- 


1181 


04862 


20 


5691 


066 1 3 


i5 


1222 


i3 


48 


01396 


7*' 


6i5i 


o3i43 


Si- 


820D 


04891 


20 


4465 


06642 


i5 


o557 


12 


49 


01425 


70- 


1 533 


03172 


Si- 


5284 


04920 


20 


3253 


06671 


14 


9898 


n 


5o 


oi455 


68- 


75oi 


03201 


3i- 


2416 


04949 


20 


2o56 


06700 


14 


9244 


10 


5i 


01484 


67. 


4019 


o323o 


3o- 


9 5 99 


04978 


20 


0872 


06730 


14 


85o6 


9 


52 


0i5i3 


66- 


IODO 


o3259 


3o- 


6833 


0D007 


J 9 


9702 


06759 


14 


7964 


8 


53 


oi542 


64- 


858o 


o3288 


3o- 


4116 


o5o37 


*9 


8546 


06788 


14 


73i7 


7 


54 


01571 


63- 


5567 


o33i7 


3o- 


1446 


o5o66 


J 9 


74o3 


06817 


14 


6685 


6 


55 


01600 


62. 


4992 


o3346 


29. 


8823 


o5o95 


*9 


6273 


06847 


14 


6059 


5 


56 


01629 


61 • 


382o 


03376 


29. 


6245 


o5i24 


*9 


5i56 


06876 


14 


5438 


4 


5 7 


oi658 


60 • 


3o58 


o34o5 


29. 


3711 


o5i53 


*9 


4o5i 


06905 


14- 


4823 


3 


58 


01687 


5 T 


2659 


o3434 


29. 


1220 


o5i82 


l 9 


2959 


06934 


i4- 


4212 


2 


5 9 


01716 


58- 


2612 


o3463 


28. 


8771 


05212 


x 9 


1879 


06963 


i4- 


3607 


1 


60 


01746 


57-2900 


03492 


28-6363 


00241 


19-0811 


06993 


14-3007 





/ 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


/ 


89° 


88° 


87° 


8 


3° 



74 NATURAL TANGENTS AND COTANGENTS. Table III. 


/ 


4° 


5° 


6° 


1° 


/ 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 





06993 


l4-3oo7 


08749 


H-43oi 


io5io 


9«5i436 


12278 


8-14435 


60 


i 


07022 


14 


•241 1 


08778 


II 


• 3 9 l 9 


io54o 


9 


48781 


I23o8 


8 


12481 


5 9 


2 


07051 


14 


1821 


08807 


11 


• 354o 


10569 


9 


46l4l 


12338 


8 


io536 


58 


3 


07080 


14 


1235 


08837 


11 


• 3i63 


10599 


9 


435i5 


12367 


8 


08600 


57 


4 


07110 


U 


o655 


08866 


11 


• 2789 


10628 


9 


40904 


12397 


8 


06674 


56 


5 


O7i3o 


14 


0079 


o88 9 5 


11 


•2417 


10657 


9 


38307 


12426 


8 


04756 


55 


6 


07168 


i3 


9507 


08925 


11 


• 2048 


10687 


9 


35724 


12456 


8 


02848 


54 


7 


07197 


i3 


8940 


08954 


11 


• 1681 


1 07 1 6 


9 


33i54 


12485 


8 


00948 


53 


8 


07227 


i3 


83 7 8 


o8 9 83 


1 1 


• i3i6 


10746 


9 


30599 


I25i5 


7 


99058 


52 


9 


07256 


i3 


7821 


09013 


n 


• 0954 


10775 


9 


28o58 


12544 


7 


97176 


5i 


10 


07285 


i3 


7267 


09042 


11 


• 0694 


io8o5 


9 


2553o 


12574 


7 


•95302 


5o 


ii 


oi3i4 


i3 


6719 


09071 


1 1 


•0237 


io834 


9 


23oi6 


i26o3 


7 


• 9 3438 


49 


12 


o 7 344 


i3 


6174 


09101 


10 


.9882 


io863 


9 


2o5i6 


12633 


7 


• 9 i582 


48 


i3 


07373 


i3 


5634 


09l3o 


10 


■ 9 52 9 


io8 9 3 


9 


18028 


12662 


7 


•89734 


47 


14 


07402 


i3 


5o 9 8 


09159 


10 


;?i78 


10922 


9 


i5554 


12692 


7 


•87895 


46 


i5 


07431 


i3 


4566 


09189 


10 


• 8829 


10952 


9 


13093 


12722 


7 


•86064 


45 


16 


07461 


i3 


4o3q 


09218 


10 


• 8483 


10981 


9 


10646 


12751 


7 


•84242 


44 


17 


07490 


i3 


35i5 


09247 


10 


• 8i3 9 


IIOII 


9 


08211 


12781 


7 


•82428 


43 


18 


07519 


i3 


2996 


09277 


10 


•7797 


1 1 040 


9 


05789 


12810 


7 


•80622 


42 


J 9 


07548 


i3 


2480 


093o6 


10 


•745 7 


1 1 070 


9 


03379 


12840 


7 


•78825 


4i 


20 


07578 


1 3 


1969 


09335 


10 


• 7119 


1 1 099 




00983 


12869 


7 


•77035 


4o 


21 
j 22 


07607 


i3 


1461 


09365 


10 


•6783 


11128 


8 


9 85 9 8 


12899 


7 


•76254 


ll 


07636 


i3 


o 9 58 


09394 


10 


•645o 


iii58 


8 


■96227 


12929 


7 


•73480 


23 


07665 


i3 


0458 


09423 


10 


•6118 


11187 


8 


• 9 386 7 


12958 


7 


•71715 


37 


24 


07695 


12 


9962 


09453 


10 


•5789 


11217 


8 


•91520 


12988 


7 


•69957 


36 


25 


07724 


12 


9469 


09482 


10 


•5462 


1 1 246 


8 


•8 9 i85 


13017 


7 


.68208 


35 


26 


07753 


12 


8981 


0951 1 


10 


•5i36 


11276 


8 


•86862 


i3o47 


7 


•66466 


34 


27 


07782 


12 


8496 


09541 


10 


•48i3 


n3o5 


8 


•8455i 


13076 


7 


•64732 


33 


28 


07812 


12 


8014 


09570 


10 


•4491 


n335 


8 


■82252 


i3io6 


7 


•63oo5 


32 


29 


07841 


12 


7536 


09600 


10 


•4172 


1 1 364 


8 


•79964 


i3i36 


7 


•61287 


3i 


3o 


07870 


12 


7062 


09629 


10 


•3854 


1 1394 


8 


•77689 


i3i65 


7 


•59575 


3o 


3i 


07899 


12 


6591 


0g658 


10 


• 3538 


1 1423 


8 


•75425 


i3i9D 


7 


•57872 


29 


32 


07929 


12 


6124 


09688 


10 


•3224 


II452 


8 


•73172 


l3224 


7 


• 56i 7 6 


28 


33 


07958 


12 


566o 


09717 


10 


•2913 


1 1482 


8 


70931 


13254 


7 


•54487 


27 


34 


07987 


12 


5199 


09746 


10 


• 2602 


ii5ii 


8 


68701 


i3284 


7 


•52806 


26 


35 


08017 


12 


4742 


09776 


10 


•2294 


ii54i 


8 


66482 


i33i3 


7 


•5u32 


25 


36 


08046 


12 


4288 


09805 


10 


• 1988 


1 1 570 


8 


64275 


1 3343 


7 


•49465 


24 


37 


08075 


12 


3838 


09834 


10 


•1 683 


1 1 600 


8 


62078 


13372 


7 


•47806 


23 


38 


08104 


12 


3390 


09864 


10 


• i38i 


11629 


8 


5 9 8 9 3 


1 3402 


7 


•46i54 


22 


3 9 


o8i34 


12 


2946 


09893 


10 


•1080 


1 1659 


8 


57718 


1 343 2 


7 


•44509 


21 


4o 


08 1 63 


12 


25o5 


O9923 


10 


•0780 


11688 


8 


55555 


1 346 1 


7 


•42871 


20 


41 


08192 


12 


2067 


09952 


10 


•o483 


11718 


8 


53402 


1 349 1 


7 


•41240 


IO 


42 


08221 


12 


i632 


09981 


10 


•0187 


1 1747 


8 


5i25o 


i352i 


7 


•39616 


l8 


43 


08251 


12 


1201 


IOOII 


9- 


98930 


11777 


8 


49128 


i355o 


7 


.37999 


17 


44 


08280 


12 


0772 


10040 


9- 


76007 


1 1 806 


8 


47007 


i358o 


7 


3638 9 


16 


45 


08309 


12 


o346 


10069 


9- 


j3ioi 


1 1 836 


8 


44896 


13609 


7 


34786 


i5 


46 


o833 9 




9923 


10099 


9- 


302 1 1 


1 1 865 


8 


42795 


i363 9 


7 


33190 


14 


47 


o8368 




9D04 


10128 


9- 


3 7 338 


n8 9 5 


8 


40705 


i366 9 


7 


3 1 600 


i3 


48 


08397 




9087 


ioi58 


9- 


34482 


11924 


8 


38625 


i36 9 8 


7 


3ooi8 


12 


i 9 


08427 




86 7 3 


10187 


9- 


3i64i 


1 1954 


8 


36555 


13728 


7 


28442 


11 


5o 


o8456 




8262 


10216 


9- 


78817 


11983 


8 


34496 


i3758 


7 


26873 


10 


5i 


08480 




7853 


10246 


9* 


76009 


I20l3 


8 


32446 


i3 7 8 7 


7 


253io 


9 


52 


o85i4 




7448 


10275 


9* 


73217 


12042 


8 


3o4o6 


i38i 7 


7 


23754 


8 


53 


o8544 




7045 


io3o5 


9- 


70441 


12072 


8 


28376 


1 3846 


7 


22204 


7 


54 


08573 




6645 


io334 


9' 


37680 


I2I0I 


8 


26355 


i38 7 6 


7 


20661 


6 


56 


08602 




6248 


io363 


9- 


54935 


I2l3l 


S 


24345 


13906 


7 


19125 


5 


56 


o8632 




5853 


10393 


9- 


32205 


I 2l6o 


8- 


22344 


i3 9 35 


7 


17594 


4 


5 7 


08661 




546i 


10422 


9- 


29490 


MI 90 


8- 


20352 


i3 9 65 


7- 


1 607 1 


3 


58 


08690 




5072 


10452 


9- 


3679I 


I22I9 


8 


18370 


13995 


7- 


14553 


2 


5 9 


08720 




4685 


1 048 1 


9' 


54l06 


I 2 24Q 


8- 


i63 9 8 


14024 


7- 


i3o42 


1 


60 


08749 


ii-43oi 


io5io 


9-5i436 


12278 


8-14435 


i4oD4 


7 * i i537 





t 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


/ 


8 


5° 


84° 


83° 


8 


2° 













Table III. NATURAL TANGENTS AND COTANGENTS. 75 

— . 


/ 


8° 


9° 


10° 


11° 


/ 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 





Uo54 


7 • 1 1 537 


15838 


6.3l375 


17633 


5-67128 


I 9 438 


5-14455 


60 


i 


U084 


7 


ioo38 


1 5868 


6 


30189 


17663 


5 


66 1 65 


I9468 


5 


i3658 


5 9 


2 


I4n3 


7 


08546 


i58 9 8 


6 


29007 


17693 


5 


652o5 


19498 


5 


12862 


58 


3 


I4i43 


7 


07059 


i5 9 28 


6 


27829 


17723 


5 


64248 


I9529 


5 


12069 


5 7 I 


4 


I4I73 


7 


o5579 


i5 9 58 


6 


26655 


17753 


5 


63295 


I9559 


5- 


11279 


56 I 


5 


14202 


7 


o4io5 


1 5 9 88 


6 


25486 


I 77 83 


5 


62344 


I9589 


5 


10490 


55 1 


6 


14232 


7 


02637 


16017 


6 


24321 


I 7 8l3 


5 


6 1 3 97 


19619 


5 


09704 


54 


7 


14262 


7 


01174 


16047 


6 


23i6o 


17843 


5 


6o452 


19649 


5 


00921 


53 


8 


14291 


6 


99718 


16077 


6 


22003 


17873 


5 


5961 1 


I9680 


5 


08139 


52 


9 


14321 


6 


98268 


16107 


6 


2o85i 


17903 


5 


585 7 3 


19710 


5 


07360 


5i 


10 


i435i 


6 


96823 


16137 


6 


19703 


17933 


5 


57638 


19740 


5 


o6584 


5o 


ii 


i438i 


6 


9 5385 


16167 


6 


18559 


17963 


5 


56706 


I9770 


5 


05809 


49 


12 


14410 


6 


93952 


16196 


6 


17419 


17993 


5 


55777 


I980I 


5 


o5o37 


48 


i3 


i444o 


6 


92D25 


16226 


6 


16283 


18023 


5 


5485 1 


i 9 83i 


5 


04267 


47 


14 


14470 


6 


91104 


16256 


6 


i5i5i 


i8o53 


5 


53927 


1 986 1 


5 


03499 


46 


i5 


14499 


6 


89688 


16286 


6 


14023 


i8o83 


5 


53oo7 


19891 


5 


027M 


45 


16 


14529 


6 


88278 


i63i6 


6 


12899 


i8ii3 


5 


52090 


19921 


5 


01971 


44 I 


n 


14559 


6 


86874 


i6346 


6 


11779 


18143 


5 


51176 


19952 


5 


01210 


43 | 


18 


14588 


6 


85475 


i63 7 6 


6 


io664 


18173 


5 


5o264 


19982 


5 


oo45 1 


42 1 


J 9 


14618 


6 


84082 


i64o5 


6 


09552 


18203 


5 


49356 


20012 


4 


99695 


4i 1 


20 


14648 


6 


82694 


i6435 


6 


08444 


18233 


5 


4845 1 


20042 


4 


98940 


40 


21 


14678 


6 


8i3i2 


1 6465 


6 


07340 


18263 


5 


47548 


20073 


4 


98188 


39 


22 


14707 


6 


79936 


16495 


6 


06240 


18293 


5 


46648 


20103 


4 


97438 


38 


23 


14737 


6 


78564 


i6525 


6 


o5i43 


i8323 


5 


4575i 


2oi33 


4 


96690 


37 


24 


14767 


6 


77199 


i6555 


6 


040 5 1 


18353 


5 


4485 7 


20164 


4 


95945 


36 


25 


I479 6 


6 


7 5838 


i6585 


6 


02962 


i8383 


5 


43966 


20194 


4 


95201 


35 


26 


14826 


6 


74483 


i66i5 


6 


01878 


18414 


5 


43077 


20224 


4 


94460 


34 


27 


14856 


6 


73i33 


i6645 


6 


00797 


18444 


5 


42192 


20254 


4 


93721 


33 


28 


14886 


6 


71789 


16674 


5 


99720 


18474 


5 


41309 


20285 


4 


92984 


32 


29 


U9i5 


6 


70450 


16704 


5 


98646 


i85o4 


5 


40429 


2o3i5 


4 


92249 


3i 


3o 


14945 


6 


69116 


16734 


5 


97576 


i8534 


5 


39552 


2o345 


4 


9i5i6 


3o 


3i 


14975 


6 


67787 


16764 


5 


965io 


1 8564 


5 


38677 


20376 


4 


90785 


29 


32 


i5oo5 


6 


66463 


16794 


5 


95448 


i85 9 4 


5 


378o5 


20406 


4 


90o56 


28 


33 


i5o34 


6 


65 1 44 


16824 


5 


94390 


18624 


5 


36 9 36 


2o436 


4 


89330 


27 


34 


i5o64 


6 


6383 1 


i6854 


5 


9 3335 


1 8654 


5 


36070 


20466 


4 


886o5 


26 


35 


1 5094 


6 


62523 


16884 


5 


92283 


18684 


5 


352o6 


20497 


4 


87882 


25 


36 


i5i24 


6 


61219 


16914 


5 


91235 


18714 


5 


34345 


20527 


4 


87162 


24 


37 


i5i53 


6 


59921 


16944 


5 


90191 


18745 


5 


33487 


2o557 


4 


86444 


23 


38 


i5i83 


6 


58627 


16974 


5 


8 9 i5i 


18775 


5 


3263i 


2o588 


4 


85727 


22 


3 9 


i52i3 


6 


57339 


17004 


5 


88114 


i88o5 


5 


3i 77 8 


20618 


4 


85oi3 


21 


40 


i5243 


6 


56o55 


17033 


5 


87080 


i8835 


5 


30928 


20648 


4 


843oo 


20 


4i 


15272 


6 


54777 


17063 


5 


86o5i 


i8865 


5 


3oo8o 


20679 


4 


835 9 o 


19 


42 


i53o2 


6 


535o3 


17093 


5 


85o24 


i88 9 5 


5 


29235 


20709 


4 


82882 


IO 


43 


i5332 


6 


52234 


17123 


5 


84001 


18925 


5 


28393 


20739 


4 


82175 


17 


44 


i5362 


6 


50970 


i7i53 


5 


82982 


i8 9 55 


5 


27553 


20770 


4 


814.71 


16 


45 


15391 


6 


49710 


17183 


5 


81966 


18986 


5 


26715 


20800 


4 


80769 


i5 


46 


1 542 1 


6 


48456 


17213 


5 


80953 


19016 


5 


2588o 


2o83o 


4 


80068 


14 


47 


1 545 1 


6 


47206 


17243 


5 


79944 


19046 


5 


25o48 


20861 


4 


79370 


i3 


48 


1 548 1 


6 


45961 


17273 


5 


78938 


19076 


5 


24218 


20891 


4 


78673 


12 


49 


i55ii 


6 


44720 


i73o3 


5 


77936 


19106 


5 


23391 


20921 


4 


77978 


11 


5o 


1 554o 


6 


43484 


17333 


5 


76937 


19136 


5 


22566 


20952 


4 


77286 


10 


5i 


15570 


6 


42253 


17363 


5 


75941 


19166 


5 


21744 


20982 


4 


76595 


9 


52 


i56oo 


6 


41026 


17393 


5 


74949 


19197 


5 


20925 


2IOl3 


4 


75906 


8 


53 


i563o 


6 


3 9 8o4 


17423 


5 


73960 


19227 


5 


20107 


21043 


4 


75219 


7 


54 


i566o 


6 


38587 


17453 


5 


72974 


19257 


5 


19293 


21073 


4 


74534 


6 


55 


i568 9 


6 


3 7 3 7 4 


i 7 483 


5 


71992 


19287 


5 


18480 


21 104 


4 


7 385i 


5 


56 


i5 7 i 9 


6 


36i65 


17D13 


5 


7ioi3 


19317 


5 


17671 


2ii34 


4 


73170 


4 


5 1 


15749 


6 


34961 


17543 


5 


70037 


19347 


5 


1 6863 


21164 


4 


72490 


3 


58 


1D779 


6 


33 7 6i 


17573 


5 


69064 


i 9 3 7 8 


5 


i6o58 


21195 


4 


71813 


2 


5 9 


i58o 9 


6 


32566 


17603 


5 


68094 


19408 


5 


i5256 


21225 


4 


7"37 


1 


60 


i5838 


6-3i375 


17633 


5-67128 


i 9 438 


5-14455 


21256 


4-70463 





/ 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


/ 


81° 


80° 


19° 


78° 



16 NATURAL TANGENTS AND COTANGENTS. Table III. 


/ 


12° 


13° 


14° 


15° 


/ 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 





21256 


4-70463 


23o87 


4-33i48 


24933 


4-01078 


26795 


3-732o5 


60 


i 


21286 


4- 


69791 


23l 17 


4-32573 


24964 


4- 


oo582 


26826 


3- 


72771 


5 9 


2 


2i3i6 


4 


69121 


23 1 48 


4-32ooi 


24995 


4- 


00086 


26857 


3 


72338 


58 


3 


2 1 347 


4- 


68452 


23179 


4-3i43o 


25026 


3 


99592 


26888 


3 


71907 


57 


4 


2l377 


4- 


67786 


23209 


4-3o86o 


25o56 


3 


99099 


26920 


3 


7U76 


56 


5 


21408 


4- 


671 21 


23240 


4-30291 


25087 


3 


98607 


26951 


3 


71046 


55 


6 


2U38 


4- 


66458 


23271 


4-29724 


25n8 


3 


98117 


26982 


3 


70616 


54 


7 


21469 


4 


65797 


233oi 


4-29159 


25i49 


3 


97627 


27013 


3 


70188 


53 


8 


21499 


4 


65i38 


23332 


4-28595 


25i8o 


3 


97i39 


27044 


3 


69761 


5 2 


9 


21529 


4 


64480 


23363 


4- 28032 


252II 


3 


96651 


27076 


3 


6o335 


5i 


10 


2i56o 


4 


63825 


23393 


4-27471 


25242 


3 


96165 


27107 


3 


68909 


5o 


ii 


21590 


4 


63171 


23424 


4-26911 


25273 


3 


9 568o 


27138 


3 


68485 


49 


12 


21621 


4 


625i8 


23455 


4-26352 


253o4 


3 


95196 


27169 


3 


68061 


48 


i3 


2i65i 


4 


61868 


23485 


4-25795 


25335 


3 


947i3 


27201 


3 


67638 


47 


14 


21682 


4 


61219 


235i6 


4-25239 


25366 


3 


94232 


27232 


3 


67217 


46 


i5 


21712 


4 


60572 


23547 


4-24685 


25397 


3 


93751 


27263 


3 


66796 


45 


16 


21743 


4 


59927 


23578 


4-24i32 


25428 


3 


93271 


27294 


3 


663 7 6 


44 


n 


21773 


4 


5 9 283 


236o8 


4-2358o 


25459 


3 


92793 


27326 


3 


65957 


43 


18 


21804 


4 


5864i 


23639 


4-23o3o 


25490 


3 


92316 


27357 


3 


65538 


42 


19 


2i834 


4 


58ooi 


23670 


4-22481 


25521 


3 


91839 


27388 


3 


65i2i 


4i 


20 


21864 


4 


5 7 363 


23700 


4-21933 


25552 


3 


91364 


27419 


3 


64705 


4o 


21 


21895 


4 


56726 


2373i 


4-21387 


25583 


3 


90890 


2745i 


3 


64289 


3? 


22 


21925 


4 


56091 


23762 


4-20842 


256i4 


3 


90417 


27482 


3 


63874 


23 


21956 


4 


55458 


23793 


4-20298 


25645 


3 


89945 


27513 


3 


6346i 


37 


H 


21986 


4 


54826 


23823 


4-19756 


25676 


3 


89474 


27D45 


3 


63o48 


36 


25 


22017 


4 


54196 


23854 


4-19215 


25707 


3 


89004 


27576 


3 


62636 


35 


26 


22047 


4 


53568 


23885 


4-18675 


25 7 38 


3 


88536 


27607 


3 


62224 


34 


11 


22078 


4 


52941 


23916 


4-18137 


25769 


3 


88068 


27638 


3 


61814 


33 


22108 


4 


523i6 


23946 


4-17600 


258oo 


3 


87601 


27670 


3 


6i4o5 


32 


2 , 9 


22139 


4 


51693 


23977 


4-17064 


2583i 


3 


87136 


27701 


3 


60996 


3i 


3o 


22169 


4 


51071 


24008 


4-i653o 


25862 


3 


86671 


27732 


3 


6o588 


3o 


3i 


22200 


4 


5o45i 


24039 


4- 1 5 99 7 


258 9 3 


3 


86208 


27764 


3 


60181 


29 


32 


2223l 


4 


49832 


24069 


4-i5465 


25924 


3 


85745 


27795 


3 


59775 


28 


33 


2226l 


4 


492 1 5 


24100 


4-I4934 


25955 


3 


85284 


27826 


3 


59370 


27 


34 


22292 


4 


48600 


24i3i 


4-i44o5 


25 9 86 


3 


84824 


2 7 858 


3 


58 9 66 


26 


35 


22322 


4 


47986 


24162 


4-i38 77 


26017 


3 


84364 


27889 


3 


58562 


25 


36 


22353 


4 


47374 


24193 


4-i335o 


26048 


3 


83 9 o6 


27920 


3 


58i6o 


24 


37 


22383 


4 


46764 


24223 


4-12825 


26079 


3 


83449 


27952 


3 


57758 


23 


38 


22414 


4 


46i55 


24254 


4-i23oi 


26110 


3 


82992 


27983 


3 


57357 


22 


3 9 


22444 


4 


45548 


24285 


4-11778 


26141 


3 


82537 


28oi5 


3 


56957 


21 


4o 


22475 


4 


44942 


243i6 


4-U256 


26172 


3 


82083 


28046 


3 


56557 


20 


4i 


225o5 


4 


44338 


24347 


4-10736 


26203 


3 


8i63o 


28077 


3 


56 1 59 


IO 


42 


22536 


4 


43735 


24377 


4-10216 


26235 


3 


81177 


28109 


3 


55 7 6i 


18 


43 


22567 


4 


43 1 34 


24408 


4-09699 


26266 


3 


80726 


28140 


3 


55364 


x 7 


44 


22597 


4 


42534 


24439 


4-09182 


26297 


3 


80276 


28172 


3 


54968 


16 


45 


22628 


4 


41936 


24470 


4-08666 


26328 


3 


79827 


28203 


3 


54573 


i5 


46 


22658 


4 


4i34o 


245oi 


4-o8i52 


26359 


3 


79 3 7 8 


28234 


3 


54i79 


U 


47 


22689 


4 


40745 


24532 


4-07639 


26390 


3 


78931 


28266 


3 


53785 


i3 


48 


22719 


4 


401 52 


24562 


4-07127 


26421 


3 


78485 


28297 


3 


533 9 3 


12 


i 9 


22750 


4 


39560 


24593 


4-06616 


26452 


3 


78040 


28329 


3 


53ooi 


11 


5o 


22781 


4 


38969 


24624 


4-06107 


26483 


3 


77 5o5 


2836o 


3 


•52609 


10 


5i 


22811 


4 


3838i 


24655 


4- 05599 


265i5 


3 


77152 


28391 


3 


•52219 


9 


52 


22842 


4 


37793 


24686 


4-05092 


26546 


3 


76709 


28423 


3 


•51829 


8 


53 


22872 


4 


37207 


24717 


4-04586 


26577 


3 


76268 


28454 


3 


5i44i 


7 


54 


22903 


4 


36623 


24747 


4 -04081 


26608 


3 


75828 


28486 


3 


5io53 


6 


55 


22934 


4 


• 36o4o 


24778 


4-03578 


26639 


3 


7 5388 


28517 


3 


5o666 


5 


56 


22964 


4 


•35459 


24809 


4-o3o75 


26670 


3 


74o5o 


28549 


3 


50279 


4 


5 7 


22995 


4 


.34879 


24840 


4-02574 


26701 


3 


745i2 


2858o 


3 


49894 


3 


58 


23026 


4 


343oO 


24871 


4-02074 


26733 


3 


74075 


28612 


3 


49509 


2 


5 9 


23o56 


4 


•33723 


24902 


4-01576 


26764 


3 


73640 


28643 


3 


4oi25 


1 


60 


23087 4-33U8 


24933 


4*01078 


26795 


3 


732o5 


28675 


3-48741 





/ 


Cotang. 1 Tangent. 


Cotang. 


Tangent. 


Cotang. 


T 


angent. 


Cotang. 


Tangent. 


/ 


11° 


76° 


75° 


740 







Table IIL NATURAL TANGENTS AND COTANGENTS. 77 


i 


16° 


17° 


18° 


19° 


/ 


Tangent. 


Cotang. 


Tangent.' Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


o 


28675 


3.4874J 


3o573 


3.27085 


32492 


3-07768' 


34433 


2-90421 


60 


i 


28706 


3 


483 5 9 


3o6o5 


3 


26745 


32524 


3 


07464 


34465 


2 


90147 


5 9 


2 


28738 


3 


47977 


3o637 


3 


26406 


32556 


3 


07160 


34498 


2 


8 9 3 7 3 


58 


3 


28769 


3 


47396 


30669 


3 


26067 


32588 


3 


06857 


34530 


2 


89600 


57 


4 


28800 


3 


47216 


30700 


3 


25729 


32621 


3 


06554 


34563 


2 


89327 


56 


5 


28832 


3 


46837 


30732 


3 


253o2 


32653 


3 


06252 


34596 


2 


89055 


55 


6 


28864 


3 


46458 


30764 


3 


25o55 


32685 


3 


o595o 


34628 


2 


88783 


54 


7 


28893 


3 


46080 


30796 


3 


24719 


32717 


3 


o5649 


34661 


2 


885u 


53 


8 


28927 
28956 


3 


45703 


30828 


3 


24383 


32749 


3 


o5349 


34693 


2 


88240 


52 


9 


3 


45327 


3o86o 


3 


24049 


32782 


3 


o5o49 


34726 


2 


87970 


5i 


10 


28990 


3 


4495i 


30891 


3 


23714 


32814 


3 


04749 


34758 


2 


87700 


5o 


ii 


29021 


3 


44576 


30923 


3 


2338i 


32846 


3 


o445o 


34791 


2 


87430 


4§ 


12 


29053 


3 


44202 


30955 


3 


23o48 


32878 


3 


o4i52 


34824 


2 


87161 


48 


i3 


29084 


3 


43829 


30987 


3 


22715 


32911 


3 


o3854 


34856 


2 


86892 


47 


14 


29116 


3 


43456 


31019 


3 


22384 


32943 


3 


o3556 


34889 


2 


86624 


46 


i5 


29147 


3 


43o84 


3io5i 


3 


22053 


32975 


3 


o326o 


34922 


2 


86356 


45 


16 


29179 


3 


42713 


3io83 


3 


21722 


33007 


3 


02963 


34954 


2 


86089 


44 


17 


29210 


3 


42343 


3iii5 


3 


21392 


33o4o 


3 


02667 


34987 


2 


85822 


43 


18 


29242 


3 


41973 


3ii47 


3 


21063 


33072 


3 


02372 


35oi9 


2 


85555 


42 


19 


29274 


3 


41604 


31178 


3 


20734 


33 1 04 


3 


02077 


35o52 


2 


8528 9 


41 


20 


293o5 


3 


41236 


3l2IO 


3 


20406 


33i36 


3 


oi 7 83 


35o85 


2 


85o23 


40 


21 


29337 


3 


40869 


31242 


3 


20079 


33169 


3 


01489 


35i 17 


2 


84758 


3 9 


22 


2 9 368 


3 


4o5o2 


31274 


3 


19752 


33201 


3 


01196 


35i5o 


2 


84494 


38 


23 


29400 


3 


401 36 


3i3o6 


3 


19426 


33233 


3 


00903 


35i83 


2 


84229 


37 


24 


29432 


3 


39771 


3i338 


3 


19100 


33266 


3 


006 1 1 


352i6 


2 


83 9 65 


36 


25 


29463 


3 


39406 


31370 


3 


18775 


33298 


3 


00319 


35248 


2 


83702 


35 


26 


29495 


3 


39042 


3 1402 


3 


1 845 1 


3333o 


3 


00028 


3528i 


2 


8343 9 


34 


3 


29526 


3 


386 79 


3 1 434 


3 


18127 


33363 


2 


99738 


353i4 


2 


83 1 76 


33 


29558 


3 


383q 


3i466 


3 


17804 


33395 


2 


99447 


35346 


2 


82914 


32 


?9 


29590 


3 


37955 


31498 


3 


1 7481 


33427 


2 


99 1 58 


35379 


2 


82653 


3i 


3o 


29621 


3 


37094 


3i53o 


3 


17159 


3346o 


2 


98868 


35412 


2 


82391 


3o 


3i 


29653 


3 


37234 


3 1 562 


3 


i6838 


33492 


2 


9 858o 


35445 


2 


82i3o 


29 


32 


2 9 685 


3 


36875 


3i5 9 4 


3 


16517 


33524 


2 


98292 


35477 


2 


81870 


28 


33 


29716 


3 


365i6 


31626 


3 


16197 


33557 


2 


98004 


355io 


2 


81610 


27 


34 


29748 


3 


36 1 58 


3i658 


3 


i58 77 


3358 9 


2 


97717 


35543 


2 


8i35o 


26 


35 


29780 


3 


358oo 


31690 


3 


15558 


33621 


2 


9743o 


355 7 6 


2 


81091 


25 


36 


29811 


3 


35443 


31722 


3 


1 524o 


33654 


2 


97144 


356o8 


2 


8o833 


24 


37 


29843 


3 


35087 


31754 


3 


14922 


33686 


2 


9 6858 


35641 


2 


80074 


23 


38 


29875 


3 


34732 


3i 7 86 


3 


U6o5 


33 7 i8 


2 


96573 


35674 


2 


8o3i6 


22 


3 9 


29906 


3 


34377 


3i8i8 


3 


14288 


3375i 


2 


96288 


35707 


2 


80059 


21 


4o 


29938 


3 


34023 


3i85o 


3 


13972 


33783 


2 


96004 


35740 


2 


79802 


20 


4i 


29970 


3 


33670 


3i88 2 


3 


13656 


338i6 


2 


95721 


35772 


2 


79545 


IQ 


42 


3oooi 


3 


333i7 


31914 


3 


i334i 


33848 


2 


95437 


358o5 


2 


79289 


10 


43 


3oo33 


3 


32965 


3 1 946 


3 


13027 


3388i 


2 


95i55 


35838 


2 


79033 


17 


44 


3oo65 


3 


32614 


3i 97 8 


3 


12713 


339i3 


2 


94872 


35871 


2 


78778 


16 


45 


30097 


3 


32264 


32010 


3 


12400 


33945 


2 


94590 


35904 


2 


78523 


i5 


46 


30128 


3 


3ioi4 


32042 


3 


12087 


33978 


2 


943oo 


35 9 3 7 


2 


78269 


14 


% 


3oi6o 


3 


3 1 565 


32074 


3 


11775 


34oio 


2 


94028 


35969 


2 


78014 


i3 


30192 


3 


3i2i6 


32106 


3 


1 1464 


34043 


2 


93748 


36oo2 


2 


77761 


12 


i 9 


30224 


3 


3o868 


32139 


3 


11 153 


34075 


2 


93468 


36o35 


2 


77507 


11 


5o 


3o255 


3 


3o52i 


32171 


3 


10842 


34108 


2 


93189 


36o68 


2 


77204 


10 


5i 


30287 


3 


30174 


32203 


3 


io532 


34140 


2 


92910 


36ioi 


2 


77002 


9 


52 


3o3i9 


3 


29829 


32235 


3 


10223 


34h3 


2 


92632 


36i34 


2 


76750 


8 


53 


3o35i 


3 


2 9 483 


32267 


3 


09914 


342o5 


2 


92354 


36i6 7 


2 


76498 


7 


54 


3o382 


3 


29139 


32299 


3 


09606 


34238 


2 


92076 


36199 


2 


76247 


6 


55 


3o4i4 


3 


28795 


3233i 


3 


09298 


34270 


2 


91799 


36 2 3 2 


2 


75996 


5 


56 


3o446 


3 


28402 


32363 


3 


08991 


343o3 


2 


9i523 


36265 


2 


75746 


4 


57 


30478 


3 


28109 


32396 


3 


o8685 


34335 


2 


91246 


36298 


2 


75496 


3 


58 


3o5o9 


3 


27767 


32428 


3 


08379 


34368 


2 


90971 


3633i 


2 


70246 


2 


5 9 


3o54i 


3 


27426 


32460 


3 


08073 


344oo 


2 


90696 


36364 


2 


74997 


1 


6o 


3o573 


3-27085 


32492 


3-07768 


34433 


2-90421 


363 9 7 


2-74748 





/ 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


/ 


73° 


72° 


71° 


70° 



78 NATURAL TANGENTS AND COTANGENTS. Table III. 


/ 


20° 


21° 


22° 


23° 


/ 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 





36397 


2-74748 


38386 


2«6o5o9 


4o4o3 


2'475o9 


42447 


2-35585 


60 


i 


3643o 


2 


74499 


38420 


2 


60283 


40436 


2 


47302 


42482 


2 


353 9 5 


5 9 


2 


36463 


2 


7425i 


38453 


2 


6oo57 


40470 


2 


47095 


425i6 


2 


352o5 


58 


3 


36496 


2 


74004 


38487 


2 


5 9 83i 


4o5o4 


2 


46888 


4255i 


2 


35oi5 


5 7 


4 


36529 


2 


73756 


38520 


2 


59606 


4o538 


2 


46682 


42585 


2 


34825 


56 


5 


36562 


2 


73509 


38553 


2 


5 9 38i 


40572 


2 


46476 


42619 


2 


•34636 


55 


6 


365g5 


2 


73263 


38587 


2 


59156 


40606 


2 


46270 


42654 


2 


•34447 


54 


7 


36628 


2 


73017 


38620 


2 


58 9 32 


40640 


2 


46o65 


42688 


2 


•34258 


53 


8 


3666i 


2 


72771 


38654 


2 


58708 


40674 


2 


45860 


42722 


2 


•34069 


52 


9 


366 9 4 


2 


72526 


38687 


2 


58484 


40707 


2 


45655 


42757 


2 


•3388i 


5i 


10 


36727 


2 


72281 


38 7 2i 


2 


58261 


40741 


2 


4545 1 


42791 


2 


•336 9 3 


5o 


ii 


36760 


2 


72o36 


38754 


2 


58o38 


40775 


2 


45246 


42826 


2 


•335o5 


49 


12 


36793 


2 


71792 


38787 


2 


57815 


40809 


2 


45o43 


42860 


2 


•333i7 


48 


i3 


36826 


2 


71548 


38821 


2 


57593 


40843 


2 


4483 9 


42894 


2 


•33i3o 


47 


14 


3685 9 


2 


7i3o5 


38854 


2 


57371 


40877 


2 


44636 


42929 


2 


•32943 


46 


i5 


368 9 2 


2 


71062 


38888 


2 


57150 


409 1 1 


2 


44433 


42963 


2 


•32756 


45 


16 


36925 


2 


70819 


38921 


2 


56928 


40945 


2 


4423o 


42998 


2 


•32570 


44 


17 


36 9 58 


2 


70577 


38g55 


2 


56707 


40979 


2 


44027 


43o32 


2 


•32383 


43 


18 


06991 


2 


7o335 


38 9 88 


2 


56487 


4ioi3 


2 


43825 


43067 


2 


•32197 


42 


19 


37024 


2 


70094 


39022 


2 


56266 


41047 


2 


43623 


43ioi 


2 


•32012 


4i 


20 


37057 


9 


6 9 853 


39055 


2 


56o46 


41081 


2 


43422 


43 1 36 


2 


•3l826 


40 


21 


37090 


2 


69612 


39089 


2 


55827 


4iu5 


2 


43220 


43170 


2 


•3i64i 


a 


22 


37124 


2 


69371 


39122 


2 


556o8 


41149 


2 


•43019 


432o5 


2 


•3i456 


23 


37157 


2 


6 9 i3i 


39156 


2 


5538 9 


4u83 


2 


•42819 


43239 


2 


• 31271 


37 


24 


37190 


2 


68892 


39190 


2 


55i7<3 


41217 


2 


•42618 


43274 


2 


•3io86 


36 


25 


37223 


2 


68653 


39223 


2 


54952 


4i25i 


2 


•42418 


433o8 


2 


•30902 


35 


26 


37256 


2 


68414 


39257 


2 


54734 


41285 


2 


•42218 


43343 


2 


•30718 


34 


11 


37289 


2 


68175 


39290 


2 


•545i6 


4i3i9 


2 


•42019 


43378 


2 


•3o534 


33 


37322 


2 


67937 


39324 


2 


•54299 


4i353 


2 


•41819 


43412 


2 


•3o35i 


32 


29 


37355 


2 


67700 


39357 


2 


54082 


4i38 7 


2 


•41620 


43447 


2 


•30167 


3i 


3o 


37388 


2 


67462 


39391 


2 


53865 


41421 


2 


•41421 


4348i 


2 


• 29984 


3o 


3i 


37422 


2 


67225 


39425 


2 


53648 


4U55 


2 


•41223 


435i6 


2 


•29801 


29 


32 


37455 


2 


66989 


3 9 458 


2 


53432 


41490 


2 


•41025 


4355o 


2 


•29619 


28 


33 


37488 


2 


66752 


39492 


2 


53217 


4i524 


2 


•40827 


43585 


2 


• 29437 


27 


34 


37521 


2 


665i6 


39526 


2 


53ooi 


4i558 


2 


•40629 


43620 


2 


•29254 


26 


35 


37554 


2 


66281 


39559 


2 


52786 


41592 


2 


4o432 


43654 


2 


29073 


25 


36 


37588 


2 


66046 


39593 


2 


52671 


41626 


2 


40235 


4368 9 


2 


28891 


24 


37 


37621 


2 


658n 


39626 


2 


52357 


41660 


2 


4oo38 


43724 


2 


28710 


23 


38 


37654 


2 


65576 


39660 


2 


52142 


41694 


2 


3 9 84i 


43758 


2 


28528 


22 


3 9 


37687 


2 


65342 


39694 


2 


51929 


41728 


2 


39645 


43793 


2 


28348 


21 


4o 


37720 


2 


65109 


39727 


2 


517 15 


41763 


2 


39449 


43828 


2 


28167 


20 


4i 


37754 


2 


64875 


39761 


2 


5i5o2 


41797 


2 


39253 


43862 


2 


27087 


19 


42 


37787 


2 


64642 


39795 


v2 


5i28 9 


4i83i 


2 


3 9 o58 


438 97 


2 


27806 


18 


43 


37820 


2 


64410 


39829 


2 


51076 


4i865 


2 


38862 


43932 


2 


27626 


n 


44 


37853 


2 


64177 


39862 


2 


5o864 


41899 


2 


38668 


43 9 66 


2 


27447 


16 


45 


37887 


2 


63945 


39896 


2 


5o652 


41933 


2 


38473 


44ooi 


2 


27267 


i5 


46 


37920 


2 


63714 


39930 


2 


5o44o 


41968 


2 


38279 


44036 


2 


27088 


14 


47 


37953 


2 


63483 


39963 


2 


50229 


42002 


2 


38o84 


44071 


2 


26909 


i3 


48 


3 79 86 


2 


63252 


39997 


2 


5ooi8 


42o36 


2 


37891 


44io5 


2 


26730 


12 


i 9 


38020 


2 


63o2i 


4oo3i 


2 


49807 


42070 


2 


37697 


44Uo 


2 


26552 


11 


5o 


38o53 


2 


62791 


4oo65 


2 


49597 


42io5 


2 


375o4 


44i75 


2 


26374 


10 


5i 


38o86 


2 


62661 


40098 


2 


49386 


42139 


2 


373n 


44210 


2 


26196 


9 


52 


38i2o 


2 


62332 


401 3 2 


2 


49177 


42173 


2 


37118 


44244 


2 


26018 


8 


53 


38i53 


2 


62io3 


40166 


2 


48967 


42207 


2 


36925 


44279 


2 


25840 


7 


54 


38i86 


2 


61874 


40200 


2 


48 7 58 


42242 


2 


36 7 33 


443 1 4 


2 


25663 


6 


55 


38220 


2 


61646 


40234 


2 


48549 


42276 


2 


3654i 


44349 


2 


25486 


5 


56 


38253 


2 


61418 


40267 


2 


48340 


423io 


2 


36349 


44384 


2- 


25309 


4 


^ 


38286 


2 


61190 


4o3oi 


2 


48i32 


42345 • 


2 


36i58 


444i8 


2- 


25l32 


3 


58 


38320 


2 


60963 


4o335 


2 


47924 


42379 


2- 


35967 


44453 


2- 


24956 


2 


5 9 


38353 


2 


60736 


40369 


2 


4771° 


424i3 


2- 


35 77 6 


44488 


2- 


24780 


1 


60 


38386 


2-6o5o9 


4o4o3 


2'47509 


42447 


2-35585 


44523 


2 • 24604 





/ 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


/ 


69° 


68° 


67° 


66° 



Table IIL NATURAL TANGENTS AND COTANGENTS. 79 


/ 


24° 


25° 


26° 


27° 


t 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


1 
Tangent. | Cotang. 


Tangent. Cotang. 





44523 


2 • 24604 


4663 1 


2-l445l 


48773 | 2 


•o5o3o 


50953 I 


96261 


60 


i 


44558 


2 


•24428 


46666 


2 


■14288 


48809 2 


•04879 


50989 I 


•96120 


5 9 


2 


44593 


2 


•24252 


46702 


2 


•i4i25 


48845 2 


•04728 


5l026 1 


•90979 


58 


3 


44627 


2 


• 24077 


46737 


2 


i3 9 63 


4888l 2 


•04577 


5io63 1 


•95838 


57 


4 


44662 


2 


•23902 


46772 


2 


i38oi 


48917 2 


•04426 


51099 1 


•95698 


56 


5 


44t>97 


2 


•23727 


46808 


2 


i363g 


48953 2 


•04276 


5n36 1 


•90007 


55 


6 


44732 


2 


•23553 


46843 


2 


13477 


48989 2 


•04125 


51173 1 


•95417 


54 


7 


44767 


2 


•23378 


46879 


2 


i33i6 


49026 2 


•03975 


51209 1 


•95277 


53 


8 


44802 


2 


•23204 


46914 


2 


i3i54 


49062 2 


•o3825 


5i246 1 


•95137 


52 


9 


4483 7 


2 


23o3o 


46950 


2 


i2 99 3 


49O98 2 


•03675 


5i283 1 


•9^997 


5i 


10 


44872 


2 


22857 


46985 


2 


12832 


49l34 2 


•o3526 


5i3iq 1 


• 9 4858 


5o 


ii 


44907 


2 


22683 


47021 


2 


12671 


49170 2 


•03376 


5i356 1 


•94718 


49 


12 


44942 


2 


225l0 


47o56 


2 


I25ll 


49206 2 


•03227 


5i3g3 1 


.94579 


48 


i3 


44977 


2 


22337 


47092 


2 


i235o 


49242 2 


03078 


5i43o 1 


• 94440 


47 


14 


45oi2 


2 


22l64 


47128 


2 


1 2 190 


49278 2 


•02929 


51467 1 


•943oi 


46 


i5 


45o47 


2 


21992 


47i63 


2 


i2o3o 


493 1 5 2 


•02780 


5i5o3 1 


•94162 


45 


16 


45o82 


2 


21819 


47199 


2 


11871 


4935l 2 


•0263i 


5i54o 1 


•94023 


44 


17 


4D117 


2 


21647 


47234 


2 


11711 


49387 2 


•02483 


5i5 77 1 


• 9 3885! 43 


18 


45i52 


2 


21475 


47270 


2 


n552 


49423 2 


•02335 


5i6i4 1 


■93746 42 


19 


45187 


2 


2i3o4 


473o5 


2 


11392 


49459 j 2 


•02187 


5i65i ! 1 


■9.3608 I 41 


20 


45222 


2 


2 J J 3 2 


47341 


2 


H233 


49495 2 


02039 


5i688 j 1 


•93470 I 40 


21 


45257 


2 


20961 


47377 


2 


11075 


49532 2 


01891 


5i 7 24 j 1 


•93332 | 39 


22 


45292 


2 


20790 


47412 


2 


1 09 1 6 


49568 2 


01743 


5i 7 6i 1 


•93195 


38 


23 


45327 


2 


20619 


47448 


2 


io 7 58 


49604 2 


01596 


5i 79 8 1 


93057 


37 


24 


45362 


2 


20449 


47483 


2 


10600 


49640 2 


01449 


5i835 1 


92920 


36 


25 


45397 


2 


20278 


47519 


2 


10442 


49677 2 


0l302 


51872 1 


92782 


35 


26 


45432 


2 


20108 


47555 


2 


10284 


497l3 2 


ou55 


51909 1 


•92645 


34 


27 


45467 


2 


19938 


47590 


2 


10126 


49749 2 


01008 


5i 9 46 1 


•92508 


33 


28 


455o2 


2 


19769 


47626 


2 


09969 


49786 2 


00862 


5i 9 83 1 


■92371 


32 


*9 


45537 


2 


i 9 5 99 


47662 


2 


0981 1 


49822 2 


00715 


52020 I 


•92235 


3i 


3o 


45573 


2 


19430 


47698 


2 


096D4 


49^58 2 


00069 


52057 1 


■92098 


3o 


3i 


456o8 


2 


19261 


47733 


2 


09498 


49894 2 


oo423 


52094 I 


91962 


29 


32 


45643 


2 


19092 


47769 


2 


09341 


4993l 2 


00277 


52i3i 1 


91826 


28 


33 


456 7 8 


2 


18923 


47805 


2 


09184 


49967 2 


ooi3i 


52168 1 


•91690 


27 


34 


457i3 


2- 


18755 


47840 


2 


09028 


5ooo4 I 


99986 


52205 I 


91554 


26 


35 


45748 


2- 


i858 7 


47876 


2 


08872 


5oo4o 1 


99841 


52242 I 


•91418 


25 


36 


45784 


2- 


18419 


47912 


2 


08716 


50076 I 


99695 


52279 x 


•91282 


24 


37 


45819 


2- 


i825i 


47948 


2 


o856o 


5on3 1 


99500 


523i6 1 


•91147 


23 


38 


45854 


2- 


18084 


47984 


2 


o84o5 


5oi49 * 


99406 


52353 1 


•91012 


22 


3 9 


4588 9 


2- 


17916 


48019 


2 


o825o 


5oi85 1 


99261 


52390 1 


•90876 


21 


4o 


43924 


2- 


17749 


48o55 


2 


08094 


50222 1 


99116 


52427 1 


•90741 


20 


4i 


45960 


2- 


i 7 582 


48091 


2 


07939 


5o258 1 


98972 


52464 1 


90607 


IO 


42 


45995 


2- 


17416 


48127 


2 


07785 


5o295 1 


98828 


525oi 1 


90472 


18 


43 


46o3o 


2- 


17249 


48i63 


2 


07630 


5o33i 1 


98684 


52538 1 


90337 


17 


44 


46o65 


2 


17083 


48198 


2 


07476 


5o368 1 


98540 


52575 1 


90203 


16 


45 


46101 


2- 


16917 


48234 


2 


07321 


5 0404 1 


98396 


526i3 1 


90069 


i5 


46 


46 1 36 


2- 


i6 7 5i 


48270 


2 


07167 


5o44i 1 


98253 


5265o 1 


8 99 35 


14 


47 


46171 


2- 


i6585 


483o6 


2 


07014 


5o477 * 


98110 


52687 1 


89801 


i3 


48 


46206 


2- 


16420 


48342 


2 


06860 


5o5i4 1 


97966 


52724 1 


89667 


12 


i 9 


46242 


2- 


i6255 


48378 


2 


06706 


5o55o 1 


97823 


52761 1 


8 9 533 


11 


5o 


46277 


2- 


16090 


484U 


2 


o6553 


5o587 1 


97680 


52798 1 


89400 


10 


5i 


'463 1 2 


2- 


15925 


4845o 


2- 


06400 


5o623 1 


97538 


52836 1 


89266 


9 


52 


46348 


2- 


15760 


48486 


2- 


06247 


5o66o 1 


97395 


52873 1 


8 9 i33 


8 


53 


46383 


2- 


15596 


48521 


2- 


06094 


50696 1 


97253 


52910 1 


89000 


7 


54 


46418 


2- 


1 543 2 


48557 


2- 


00942 


5o733 1 


97m 


52947 1 


88867 


6 


55 


46454 


2- 


i5268 


48593 


2- 


o57qo 


50769 1 


96969 


52984 1 


88734 


5 


56 


46489 


2 


i5io4 


48629 


2- 


00637 


5o8o6 1 


96827 


53022 I 


88602 


4 


57 


46026 


2- 


14940 


48665 


2- 


o5485 


5o843 1 


9 6685 


53o59 1 


88469 


3 


58 


4656o 


2- 


U777 


48701 


2' 


o5333 


50879 1 


96544 


53096 1 


8833 7 


2 


5 9 


465g5 


2 


14614 


48737 


2- 


o5i82 


50916 1 


96402 


53i34 1 


88205 


1 


60 


4663 1 


2-I445I 


48773 


2- 


o5o3o 


5o953 1 


96261 


53171 i- 


88073 j 


/ 


Cotang. 


Tangent. 


Cotang. 


T 


ingent. 


Cotang. T 


ingent. 


Cotang. T 


ingent. 


/ 


6 


5° 




64° 


63° 


62° 



80 NATURAL TANGENTS AND COTANGENTS. 


Table III. 


/ 


28° 


29° 


30° 


31° 


/ 


Tangent. Cotang. 


Tangent. ( 


?otang. 


Tangent. C 


Cotang. 


Tangent. ( 


Uotang. 





53l7I I 


•88073 


5543 1 1 


•8o4o5 


5 77 35 1 


•732o5 


60086 1 


.66428 


60 


i 


53208 I 


•87941 


55469 1 


.80281 


57774 1 


•73089 


60126 I 


•663i8 


5 9 


2 


53246 I 


.87809 


55507 1 


.801 58 


57813 1 


•7297-3 


6oi65 1 


•66209 


58 


3 


53283 1 


.87677 


55545 1 


•8oo34 


5785i 1 


•72857 


6o2o5 1 


•66099 


5 7 


4 


53320 1 


.87546 


55583 1 


•79911 


57890 1 


•72741 


60245 1 


•65990 


56 


5 


53358 1 


•874l5 


55621 1 


.79788 


57929 1 


.72625 


60284 1 


•6588i 


55 


6 


533g5 1 


.87283 


55659 1 


•79665 


57968 1 


•72509 


6o324 1 


•65772 


54 


7 


53432 1 


•87152 


55697 1 


•79542 


58007 1 


•72393 


6o364 1 


•65663 


53 


8 


53470 1 


87021 


55736 1 


•79419 


58046 1 


•72278 


6o4o3 1 


•65554 


52 


9 


535o7 1 


86891 


55774 1 


•79296 


58o85 1 


•72l63 


6o443 1 


• 65445 


5i 


10 


53545 1 


86760 


558i2 1 


■79H4 


58124 1 


•72047 


6o483 1 


•6533 7 


5o 


ii 


53582 1 


8663o 


5585o 1 


•79o5i 


58162 1 


.71932 


6o522 I 


•65228 


49 


12 


53620 1 


86499 


55888 1 


78929 


58201 1 


•71817 


6o562 1 


•65i2o 


48 


i3 


53657 1 


8636 9 


55926 1 


.78807 


58240 1 


•71702 


60602 1 


•65on 


47 


i4 


53694 1 


86239 


55964 1 


78685 


58279 1 


•7i588 


60642 1 


■64903 


46 


i5 


537J2 "1 


86109 


56oo3 1 


78563 


583i8 1 


•71473 


60681 1 


•64795 


45 


16 


53769 1 


85079 


56o4i 1 


78441 


58357 1 


7i358 


60721 1 


•64687 


44 


17 


53807 1 


8585o 


56079 l 


783io 


58396 1 


71244 


60761 1 


•64579 


43 


18 


53844 1 


85720 


56117 1 


78198 


58435 1 


71129 


60801 1 


•64471 


42 


19 


53882 1 


855 9 i 


56i56 1 


78077 


58474 1 


7ioi5 


60841 i 


•64363 


41 


' 20 


53920 1 


85462 


56194 1 


77955 


585i3 1 


70901 


60881 1 


•64256 


40 


21 


53957 1 


85333 


562J2 1 


77834 


58552 1 


70787 


60921 1 


•64148 


3 9 


22 


53995 1 


85204 


56270 1 


77713 


585 9 i 1 


70673 


60960 1 


•64041 


38 


23 


54o32 1 


85075 


563o9 1 


77592 


5863 1 1 


7o56o 


61000 1 


•63934 


37 


24 


54070 1 


84946 


56347 1 


77471 


58670 1 


70446 


61040 1 


•63826 


36 


25 


54107 1 


84818 


56385 1 


7735i 


58709 1 


7o332 


61080 1 


•63719 


35 


26 


54i45 ' 1 


84689 


56424 1 


7723o 


58748 1 


70219 


61120 1 


•636i2 


34 


3 


54i83 1 


8456i 


56462 1 


77110 


58787 1 


70106 


61160 1 


•635o5 


33 


54220 1 


84433 


565oo 1 


76990 


58826 1 


69992 


61200 1 


•633 9 8 


32 


29 


54258 1 


843o5 


56539 1 


76869 


58865 1 


69879 


61240 1 


•632Q2 


3i 


3o 


54296 1 


84177 


56577 1 


76749 


58904 1 


69766 


61280 1 


•63i85 


3o 


3 1 


54333 1 


84049 


566i6 1 


7663o 


58944 1 


6 9 653 


6i320 1 


•63079 


29 


32 


54371 1 


83922 


56654 1 


76510 


58 9 83 1 


69541 


6i36o 1 


62972 


28 


33 


54409 1 


83 79 4 


566 9 3 1 


76390 


59022 1 


69428 


61400 1 


62866 


27 


34 


54446 1 


8366 7 


56 7 3i 1 


76271 


59061 1 


69316 


61440 1 


62760 


26 


35 


54484 1 • 


83540 


56769 1 


76i5i 


59101 1 


69203 


61480 1 


62654 


25 


36 


54522 i- 


834i3 


568o8 1 


76032 


59140 1 


69091 


6i52o 1 


62548 


24 


37 


5456o 1 


83286 


56846 1 


75913 


59179 1 


68979 


6i56i 1 


62442 


23 


38 


54597 1 


83i5 9 


56885 1 


75794 


59218 1 


68866 


61601 1 


62336 


22 


3 9 


54635 1 • 


83o33 


56923 1 


756 7 5 


59258 1 


68754 


61641 1 


62230 


21 


4o 


54673 1 • 


82906 


56962 1 


75556 


59297 1 


68643 


61681 1 


62125 


20 


4i 


5471 1 i- 


82780 


57000 1 


75437 


59336 1 


6853 1 


61721 1 


62019 


10 


42 


54748 1 • 


82654 


57039 1 


75319 


59376 1 


68419 


61761 1 


61914 


18 


43 


54786 1 ■ 


82528 


57078 1 


75200 


594i5 1 


683o8 


61801 1 


61808 


17 


44 


54824 1 • 


82402 


57116 1 


75082 


59454 1 


68196 


61842 1 


61703 


16 


45 


54862 1 • 


82276 


57i55 1 


74964 


59494 1 


68o85 


61882 1 


6i5 9 8 


i5 


46 


54900 1 • 


82i5o 


57193 1 


74846 


59533 1 


6 7974 


61922 1 


61493 


14 


47 


54938 1 • 


82025 


57232 i- 


74728 


59573 1 


6 7 863 


61962 1 


6i388 


i3 


48 


54973 i- 


81899 


57271 1 


74610 


59612 1 


67752 


62oo3 1 


6i283 


12 


i 9 


55oi3 i- 


8i774 


57309 1 • 


74492 


59651 1 


67641 


62043 1 


61179 


11 


5o 


55o5i i- 


81649 


57348 i- 


74375 


59691 1 


67530 


62o83 i- 


61074 


10 


01 


55089 l • 


8i524 


57386 1. 


74257 


59730 1 


67419 


62124 1 


60970 


9 


52 


55i27 i- 


81399 


57425 I- 


74Uo 


59770 1 


67309 


62164 i- 


6o865 


8 


53 


55i65 i- 


81274 


57464 1 • 


74022 


59809 1 • 


67198 


62204 i- 


60761 


7 


54 


552o3 i- 


8u5o 


575o3 1 


73905 


59849 1 ■ 


67088 


62245 I- 


60657 


6 


55 


5524i i- 


81025 


57541 I- 


73788 


5 9 888 1 • 


66978 


62285 I- 


6o553 


5 


56 


55279 1 ' 


80901 


57580 1 • 


73671 


59928 1 • 


66867 


62325 i- 


60449 


4 


57 


55317 i- 


80777 


57619 i- 


7 3555 


59967 1 • 


66757 


62366 1 • 


6o345 


3 


58 


55355 i- 


8o653 


57657 1 • 


73438 


60007 1 • 


66647 


62406 1 • 


60241 


2 


5 9 


553o3 1 


80529 


57696 1 • 


73321 


60046 "i« 


66538 


62446 1 • 


60137 


1 


60 


5543 1 i- 


8o4o5 


57735 i- 


732o5 


60086 1 • 


66428 


62487 1 • 


6oo33 





/ 


Cotang. T 


ingent. 


Cotang. | T 


ingent. 


Cotang. T 


ingent. 


Cotang. Tj 


ingent. 


/ 


61° 


60° 


59° 


58° 



Table III. 


NATURAL TANGENTS AND COTANGENTS. 81 


/ 


32° 


33° 


34° 


35° 


/ 


Tangent 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 





62487 


1 -6oo33 


64941 


I-53 9 86 


6745l 


1-48256 


70021 


I -428l5 


60 


I 


62627 


1 -59930 


64982 


1-53888 


67493 


~I-48l63 


70064 


I-42726 


5 9 


2 


62568 


1-59826 


65o23 


I -53791 


67536 


1-48070 


70107 


1-42638 


58 


3 


62608 


1-59723 


65o65 


I . 53693 


67578 


1-47977 


70i5i 


i-4255o 


57 


4 


62649 


1-59620 


65io6 


1.53595 


67620 


1-47885 


70194 


1-42462 


56 


5 


62689 


1-59517 


65i48 


1-53497 


6 7 663 


1-47792 


70238 


1-42374 


55 


6 


62730 


1-59414 


65i8 9 


i-534oo 


67705 


1-47699 


70281 


1.42286 


54 


7 


62770 


1 -593 1 1 


6523i 


i-533o2 


67748 


1-47607 


7o325 


1-42198 


53 


8 


62811 


1-59208 


65272 


i-532o5 


67790 


i-475i4 


70368 


I-42II0 


52 


9 


62802 


i-59io5 


653i4 


i-53io7 


67832 


1-47422 


70412 


1-42022 


5i 


10 


62892 


1 -5ooo2 


65355 


i-53oio 


67875 


i-4733o 


70455 


i-4iq34 


5o 


ii 


62933 


I • 50900 


65397 


1-52913 


67917 


1-47238 


70499 


1-41847 


40 


12 


62973 


1-58797 


65438 


i-528i6 


67960 


1.47U6 


70542 


i-4n 5 9 


48 


i3 


63oi4 


1 ■ 5869O 


6548o 


1-52719 


68002 


i-47o53 


70586 


1-41672 


47 


14 


63o55 


i-585 9 3 


65521 


1-52622 


68o45 


1-46962 


70629 


i- 41 584 


46 


i5 


63095 


1 • 58490 


65563 


1-52525 


68088 


1-46870 


70673 


i- 4i 497 


45 


16 


63 1 36 


1-58388 


656o4 


1-52429 


68i3o 


1-46778 


70717 


i- 4U09 


44 


17 


63 1 77 


1-58286 


65646 


1-52332 


68i 7 3 


1-46686 


70760 


I-4l322 


43 


18 


63217 


i-58i84 


65688 


1-52235 


682i5 


1-46595 


70804 


I-4I235 


42 


19 


63258 


i-58o83 


65729 


1-52x39 


68258 


i-465o3 


70848 


1-41148 


41 


20 


63299 


i- 5 79 8i 


65771 


1-52043 


683oi 


1-46411 


70891 


1 -41061 


40 


21 


6334o 


1-57879 


658i3 


i-5io46 


68343 


1-46320 


70935 


1-40974 


3 9 


22 


6338o 


1-57778 


65854 


i-5i85o 


68386 


1-46229 


70979 


1.40887 


38 


23 


63421 


1 -57676 


658 9 6 


1 -5i754 


68429 


1-46137 


71023 


1.40800 


37 


24 


63462 


1-57575 


65 9 38 


i-5i658 


68471 


1-46046 


71066 


1-40714 


36 


25 


635o3 


i- 5 7 474 


65 9 8o 


i«5i562 


685 1 4 


I-45955 


71110 


1 .40627 


35 


26 


63544 


1-57372 


66021 


I-5U66 


98557 


1-45864 


71154 


i- 40 54o 


34 


3 


63584 


1 -57271 


66o63 


i-5i37o 


68600 


I-45773 


71198 


1.40454 


33 


63625 


1 -57170 


66io5 


1 -61275 


68642 


1-45682 


71242 


1.40367 


32 


29 


63666 


1 -57069 


66147 


1 -5i 179 


68685 


1-45592 


71285 


i> 40281 


3i 


3o 


63707 


1 -56969 


66189 


i-5io84 


68728 


1 -455oi 


71329 


1-40195 


3o 


3i 


63748 


1-56868 


6623o 


1.50988 


68771 


i-454io 


7i373 


1 -40109 


29 


32 


63789 


1 -56767 


66272 


1 .50893 


68814 


1 -45320 


71417 


I -4002 2 


28 


33 


6383o 


1-56667 


663 1 4 


1.50797 


68857 


1 -45229 


71461 


i-3 9 o36 


27 


34 


638 7 i 


1-56566 


66356 


1 .50702 


68900 


1 -45i39 


7i5o5 


1 • 39850 


26 


35 


63912 


1 • 56466 


663 9 8 


1.50607 


68942 


1 -45o49 


7i549 


1-39764 


25 


36 


63 9 53 


1-56366 


66440 


i-5o5i2 


68985 


i-44o58 


71593 


1-39679 


24 


37 


63994 


1-56265 


66482 


i«5o4i7 


69028 


1-44868 


71637 


1 .39593 


23 


38 


64o35 


i-56i65 


66524 


I-5o322 


69071 


I-44778 


71681 


1 -39507 


22 


39 


64076 


i-56o65 


66566 


1.50228 


691 14 


1-44688 


71725 


1-39421 


21 


40 


641 17 


1 • 55966 


66608 


i-5oi33 


69157 


1-44598 


71769 


i-3 9 336 


20 


4i 


64i58 


1 • 55866 


6665o 


1 -5oo38 


69200 


i-445o8 


7i8i3 


1 -39260 


IQ 


42 


64199 


1 -55766 


66692 


1 .49944 


69243 


i-444i8 


7 i85 7 


1 -39165 


10 


43 


64240 


1-55666 


66734 


1-49849 


69286 


1-44329 


71901 


1-39079 


17 


44 


64281 


i-5556 7 


66776 


I-49755 


69329 


1-44239 


71946 


1.38994 


16 


45 


64322 


1-55467 


66818 


1-49661 


69372 


I-44U9 


71990 


1 .38909 


i5 


46 


64363 


1-55368 


66860 


1-49566 


69416 


1 • 44o6o 


72034 


1-38824 


14 


47 


64404 


1-55269 


66902 


1-49472 


69459 


1-43970 


72078 


1-38738 


i3 


48 


64446 


1 .55170 


66944 


1-49378 


69502 


i-4388i 


72122 


1-38653 


12 


49 


64487 


1.55071 


66986 


1-49284 


69545 


1-43792 


72166 


1-38568 


11 


5o 


64528 


1.54972 


67028 


1-49190 


6 9 588 


1 -43703 


72211 


1-38484 


10 


5i 


64069 


1.54873 


67071 


1-49097 


69631 


I-436I4 


72255 


1 .383 99 


9 


52 


64610 


1-54774 


671 1 3 


1 -49003 


69675 


1 -43525 


72299 


i-383i4 


8 


53 


64652 


1-54675 


67155 


1 -48909 


69718 


1-43436 


72344 


1-38229 


7 


54 


64693 


1.54576 


67197 


1-48816 


69761 


1-43347 


72388 


i-38i45 


6 


55 


64734 


I-54478 


67239 


1-48722 


69804 


1-43258 


72432 


i-38o6o 


5 


56 


64775 


1-54379 


67282 


1-48629 


69847 


1 • 43 1 69 


72477 


1-37976 


4 


5 1 


64817 


1-54281 


67324 


1-48536 


69891 


i-43o8o 


72521 


1-37891 


3 


58 


64858 


I- 54i83 


67366 


1-48442 


69934 


1-42992 


72565 


1-37807 


2 


5 9 


64899 


i-54o85 


67409 


1-48349 


69977 


1 -42903 


72610 


1 -37722 


1 


60 


64941 


i-53 9 86 


67451 


1-48256 


70021 


i-428i5 


72654 


i-3 7 638 





/ 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


/ 


5 


7° 


5( 


i° 


51 


)° 


5' 


t? 



4* 



82 NATURAL TANGENTS AND COTANGENTS. 


Table III 


/ 


36° 


37° 


38° 


39° 


; 


Tangent. C 


otang. 


Tangent. C 


otang. 


Tangent. C 


otang. 


Tangent. 


Cotang. 


o 


72654 I 


37638 


75355 I 


32704 


78129 I 


27994 


80978 


I • 23490 


60 


i 


72699 I 


37554 


754oi I 


32024 


78170 I 


279H 


81027 


I- 234l6 


59 


2 


72743 I 


37470 


75447 I 


32544 


78222 I 


27841 


8l0 7 5 


.1-23343 


5§ 


3 


72788 I 


3 7 386 


75492 I 


32464 


78269 I 


27764 


8u 2 3' 


4 -.23270 


57 


4 


72832 1 


37302 


75538 1 


32384 


783l6 I 


27688 


81171 


1 -23196 


56 


5 


72877 I 


37218 


75584 1 


323o4 


78363 1 


27611 


81220 


I-23I23 


55 


6 


72921 I 


3 7 i34 


7D629 1 


32224 


78410 1 


27535 


81268 


1 -23o5o 


54 


I 


72966 l< 


37o5o 


756 7 5 1 


32144 


78457 1 


27/,58 


8i3i6 


1-22977 j 53 


73oio l< 


36967 


75721 1 


32064 


78504 1 


27382 


8 1 364 


i- 22904 | 52 


9 


73o55 i< 


36883 


75767 1 


31984 


7855i 1 


27306 


8i4i3 


I-22»3l j 5l 


10 


73ioo 1 


368oo 


75812 1 


3 1 904 


78598 1 


2723o 


81461 


1-22758 


5o 


ii 


73i44 i- 


36716 


75858 1 


3i825 


78645 1 


27l53 


8i5io 


1-22685 


49 


12 


73i8 9 i- 


36633 


75904 1 


3i745 


78692 1 


27077 


8i558 


1-22612 


48 


i3 


73234 i- 


36549 


75950 1 


3 1 666 


78739 1 


27001 


81606 


1-22539 


47 ' 


14 


73278 i. 


36466 


75996 1 


3 1 586 


78786 1 


26925 


8i655 


1-22467 


46 


i5 


73323 i- 


36383 


76042 1 


3i5o7 


78834 1 


26849 


81703 


1-22394 


45 


16 


73368 1 - 


363oo 


76088 1 


31427 


78881 1 


26774 


81752 


I-2232I 


44 


17 


734i3 1- 


36217 


76134 1 


3 1 348 


78928 1 


26698 


81800 


1-22249 


43 


18 


73457 1 • 


36i33 


76180 1 


31269 


78975 1 


26622 


81849 


1-22176 


42 


19 


735o2 1 


36o5i 


76226 1 


3i 190 


79022 1 


26546 


81898 


I-22I04 


4i 


20 


73547 i- 


35 9 68 


76272 1 


3mo 


79070 1 


26471 


81946 


I-22o3l 


4o 


21 


73592 i- 


35885 


76318 1 


3io3i 


79117 1 


26395 


81995 


I-21959 


3o 


22 


73637 1. 


358o2 


76364 1 


3oo52 


79164 1 


263l9 


82044 


I- 21886 


38 


23 


7368i 1. 


35719 


76410 1 


30873 


79212 1 


26244 


82092 


1-21814 


37 


24 


73726 i« 


35637 


76456 1 


30795 


79259 1 


26169 


82141 


1 -21742 


36 


25 


73771 1. 


35554 


76502 1 


30716 


79306 1 


26093 


82190 


1-21670 


35 


26 


738i6 i- 


35472 


76548 1 


3o637 


79354 1 


26018 


82238 


1-21598 


34 


27 


7386i 1. 


35389 


76594 1 


3o558 


794oi 1 


25o43 


82287 


I-2I526 


33 


20 


73906 1 • 


353o7 


76640 1 


3o48o 


79449 1 


25867 


82336 


1-21454 


32 


V 


73951 1 


35224 


76686 1 


3o4oi 


7949 6 1 


25792 


82385 


I-2I382 


3i 


3o 


73996 1 


35i42 


76733 1 


3o323 


79544 1 


25717 


82434 


I-2l3lO 


3o 


3i 


74041 1 • 


35o6o 


76779 1 


3o244 


79591 1 


25642 


82483 


I-2I238 


29 


32 


74086 1 


34078 


76825 1 


3oi66 


79639 1 


25567 


8253i 


1-21166 


28 


33 


74i3i 1 


34896 


76871 1 


30087 


79686 1 


25492 


8258o 


1-21094 


27 


34 


74176 1 


34814 


76918 1 


30009 


79734 1 


25417 


82629 


I-2I023 


26 


35 


74221 1 


34732 


76964 1 


29931 


79781 1 


25343 


82678 


I-20o5l 25 


36 
37 


74267 1 


3465o 


77010 1 


29853 


79829 1 


25268 


82727 


1-20879 


24 


743i2 1 


34568 


77o5 7 1 


29775 


79877 i- 


25193 


82776 


I • 20808 


23 


38 


74357 1 


34487 


77103 1 


29696 


79924 1 


25n8 


82825 


I -20736 


22 


3 9 


74402 1 


344o5 


77U9 1 


29618 


79972 I 


25o44 


82874 


i-2o665 


21 


40 


74447 1 


34323 


77196 1 


29541 


80020 1 


24969 


82923 


I -20593 


20 


4i 


74492 1 


34242 


77242 1 


29463 


80067 1 


24095 


82972 


1-20522 


10 


42 


74538 1 


34160 


77289 1 


2 9 385 


8on5 1 


24820 


83022 


I -2045 I 


10 


43 


74583 1 


34079 


77335 1 


29307 


801 63 1 


24746 


83071 


I- 20379 


17 


44 


74628 1 


33998 


77382 1 


29229 


80211 1 


24672 


83i2o 


i-2o3o8 


16 


45 


74674 1 


33916 


77428 1 


29152 


8o258 1 


24597 


83i6g 


1-20237 


i5 


46 


74719 1 


33835 


77475 1 


29074 


8o3o6 1 


24523 


832i8 


I -20166 


14 


47 


74764 1 


33754 


77521 1 


28997 


8o354 1 


24449 


83268 


I • 20095 


i3 


48 


74810 1 


33673 


77568 1 


28919 


80402 1 


24376 


833i 7 


I -20024 


12 


49 


74855 1 


33592 


77615 1 


28842 


8o45o 1 


243oi 


83366 


I -19953 


11 


5o 


74900 1 


335u 


77661 1 


28764 


80498 1 


24227 


834i5 


I • 19882 


10 


5i 


74946 1 


3343o 


77708 1 


28687 


8o546 1 


24i53 


83465 


1-19811 





52 


74991 1 


33349 


77754 1 


28610 


80594 1 


24079 


835i4 


1-19740 


8 


53 


75037 1 


33268 


77801 1 


28533 


80642 1 


24oo5 


83564 


I • 19669 


7 


54 


75082 1 


33i8 7 


77848 1 


28456 


80690 1 


23931 


836i3 


1-19599 


6 


55 


75128 1 


33107 


77895 1 


28379 


80738 1 


23858 


83662 


1-19528 5 


56 


75173 1 


33o26 


77941 1 


28302 


80786 1 


23784 


83712 


1-19457 


4 


5 1 


7D219 1 


•32946 


77988 1 


28225 


8o834 1 


23710 


83761 


I -19387 


3 


I 58 


75264 1 


■32865 


78o35 1 


28148 


80882 1 


23637 


838n 


1-19316 


2 


i 9 


753io 1 


•32785 


78082 1 


28071 


80930 1 


23563 


8386o 


1-19246 


1 


60 


75355 1 


•32704 


78129 1 


•27994 


80978 1 


23490 


83910 


1-19175 





/ 


Cotang. T 


angent. 


Cotang. T 


angent. 


Cotang. T 


angent. 


Cotang. 


Tangent. 


/ 


53° 


52-° 


51° 




5 


0° 



Table III. NATURAL TANGENTS AND COTANGENTS. 83 


1 


40° 


41° 


42° 


43° 


/ 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. 


o 


83910 


1-19175 


86929 


I-l5o37 


90040 


i-iio6i 


93252 


1-07237 


60 


i 


83 9 6o 


i«i9io5 


86980 


I • 14969 


90093 


1-10996 


933o6 


1-07174 


5 9 


2 


84009 


1 -19035 


87031 


1-14902 


90146 


i-ioq3i 


9336o 


I • 07 1 1 2 


58 


3 


84069 


1-18964 


87082 


1 -14834 


90199 


1-10867 


93415 


1-07049 


57 


4 


84108 


1-18894 


87133 


1-14767 


90201 


1 -10802 


93469 


1-06987 


56 


5 


84i58 


1-18824 


87184 


1-14699 


9o3o4 


1-10737. 


93524 


1-06925 


55 


6 


84208 


1-18754 


87236 


1 -14632 


90357 


1 -10672 


93578 


I-06862 


54 


7 


84258 


1-18684 


87287 


1 -14565 


90410 


1-10607 


93633 


I -06800 


53 


8 


843o 7 


1-18614 


87338 


1-14498 


90463 


i-io543 


9 3688 


1.06738 


52 


9 


8435 7 


i- i8544 


87389 


i-i443o 


905 1 6 


1-10478 


93742 


I -06676 


5i 


10 


84407 


1-18474 


87441 


i- 1 4363 


90569 


1-10414 


9 3 797 


i-o66i3 


5o 


ii 


84457 


1-18404 


87492 


1-14296 


90621 


i- 10349 


9 3852 


i-o655i 


40 


12 


84507 


1. 18334 


87543 


1-14229 


90674 


1-10285 


93906 


1 • 06489 


48 


i3 


84556 


1-18264 


87595 


1-14162 


90727 


I-I0220 


93961 


1-06427 


2 


1 4 


84606 


1-18194 


87646 


1-14095 


90781 


i-ioi56 


94016 


i-o6365 


i5 


84656 


i-i8i25 


87698 


1-14028 


90834 


1-10091 


94071 


1 • o63o3 


45 


16 


84706 


i-i8o55 


87749 


1-13961 


90887 


1-10027 


94125 


1-06241 


44 


17 


84756 


1-17986 


87801 


i-i38 9 4 


90940 


1 -09963 


94180 


1-06179 


43 


18 


84806 


1-17916 


87852 


I-I3828 


90993 


1 -09899 


94235 


1-06117 


42 


»9 


84856 


1-17846 


87904 


1-13761 


91046 


1-09834 


94290 


1 -o6o56 


41 


20 


84906 


I-I7777 
1-17708 


87955 


1-13694 


91099 


1 -09770 


94345 


1 -06994 


40 


21 


84g56 


88007 


I- 13627 


91 153 


1 -09706 


94400 


1-05932 


3 9 


22 


85oo6 


1 -17638 


88o5 9 


1 • i356i 


91206 


1 -09642 


94455 


1 -05870 


38 


23 


85o57 


1 -17569 


88110 


i- 13494 


91259 


1 -09578 


945io 


1 -06809 


37 


24 I 85107 


i-i75oo 


88162 


i- 13428 


9i3i3 


1 -09514 


94565 


1 -05747 


36 


25 


85i5 7 


1 -i743o 


88214 


i-i336i 


9 1 366 


1 -09400 


94620 


i-o5685 


35 


26 


852o 7 


1-17361 


88265 


1-13295 


91419 


1-09386 


94676 


i-o5624 


34 


2 


85 2 5 7 


1-17292 


883 1 7 


I-I3228 


91473 


1-09322 


94731 


i-o5562 


33 


853o 7 


1-17223 


8836 9 


1 • i3i62 


91526 


1-09258 


94786 


1 -o55oi 


32 


29 


85358 


1-17154 


88421 


1-13096 


9i58o 


1-09195 


94841 


1 -06439 


3i 


3o 


854o8 


1-17085 


88473 


I-l3o2Q 


9i633 


1-09131 


94896 


1-05378 


3o 


3i 


85458 


1-17016 


88524 


1 • i 2o63 


91687 


1-09067 


94952 


i-o53i7 


29 


32 


855o 9 


1-16947 


885 7 6 


1-12097 


91740 


I-0Q003 


95007 


i-o5255 


20 


33 


8555 9 


1-16878 


88628 


I-I28JI 


9H94 


I -08940 


95062 


1 -o5io4 


27 


34 


856o 9 


1-16809 


88680 


1-12765 


91847 


1-08876 


9 5n8 


i-o5i33 


26 


35 


8566o 


1-16741 


8873? 


I -12699 


91901 


i-o88i3 


95173 


1-05072 


25 


36 


85710 


1-16672 


887S4 


1 -12633 


91955 


1 -08749 


96229 


i-o5oio 


24 


ll 


85 7 6i 


1 -i66o3 


88836 


1 -12567 


92008 


1-08686 


95284 


i- 04949 


23 


858n 


i-i6535 


88888 


I-I250I 


92062 


1-08622 


95340 


1-04888 


22 


3 9 


85862 


1 - 16466 


88940 


1 -12435 


921 16 


1 -08559 


953o5 


1-04827 


21 


4o 


85 9 i2 


i- i63 9 8 


88992 


i-i236o 


92.170 


1-08496 


95401 


1 -04766 


20 


4i 


85 9 63 


1 -zo329 


89045 


I-I230J 


92223 


i-o8432 


955o6 


1 -04706 


IQ 


42 


86014 


1-16261 


89097 


I • 12238 


92277 


1 -08369 


95562 


1 • 04644 


10 


43 


86064 


1-16192 


89149 


1-12172 


9233i 


1 -o83o6 


95618 


1-04583 


17 


44 


861 10 


1-16124 


89201 


1-12106 


9 2385 


i-o8243 


95673 


1-04522 


16 


45 


86166 


1 • i6o56 


89253 


1-12041 


92439 


1-08179 


9 5 7 2 9 


1-04461 


i5 


46 


86216 


1-15987 


8 9 3o6 


1-11975 


92493 


1 -08116 


95785 


1 -04401 


14 


47 


86267 


1-16919 


8 9 358 


1-11909 


92547 


1 -o8o53 


95841 


1 • o434o 


i3 


48 


863 1 8 


i-i585i 


89410 


1-11844 


92601 


1 -07990 


9 58 97 


1-04279 


12 


49 


86368 


I-I5783 


8 9 463 


1-11778 


92655 


1-07927 


95952 


1 • 042 1 3 


11 


5o 


86419 


1 - 13715 


8 9 5 1 5 


1-11713 


92709 


1-07864 


96008 


1 -04i 58 


10 


5i 


86470 


i-i5647 


89567 


1-11648 


92763 


1-07801 


96064 


1 • 04097 


9 


52 


86521 


i- 15579 


89620 


i-ii582 


92817 


1-07738 


96120 


1 • o4o36 


8 


53 


865 7 2 


i-i55ii 


89672 


1 • 1 i5i7 


92872 


1 -07676 


96176 


1-03976 


7 


54 


86623 


i-i5443 


89725 


i-ii452 


92926 


1-076^3 


96232 


1 -03916 


6 


55 


86674 


i-i5375 


89777 


i- 1 1387 


92980 


1 -07550 


96288 


i-o3855 


5 


56 


86725 


i-i53o8 


89830 


I • Il32I 


93o34 


1-07487 


96344 


1-03794 


4 


57 


86776 


i-i524o 


89883 


I-II256 


9 3o88 


1-07425 


96400 


i-o3734 


3 


58 


86827 


i-i5i72 


89935 


1-11191 


93i43 


1-07362 


96457 


i- 03674 


2 


5 9 


86878 


i-i5io4 


89988 


I -III26 


93197 


1 -07299 


9 65i3 


1 -o36i3 


1 


60 


86929 


1 -i5o37 


90040 


1 -11061 


93252 


1 -07237 


96569 


i-o3553 





/ 


Cotang. 


Tangent. 


Cotang. 


Tangent. 


Cotang. Tangent. 


Cotang. Tangent. 


t 


49° 


48° 


47° 


46° 



84 NATURAL TANGENTS AND COTANGENTS. Table III. 




44° 






44° 




/ 


Tangent. 


Cotang. 


/ 


1 


Tangent. 


Cotang. 


/ 





9 656o 


i«o3553 


60 


3i 


98327 


I-0I702 


29 


i 


96620 


1-03493 


5 9 


32 


98384 


I 


Ol642 


28 


2 


96681 


i-o3433 


58 


33 


98441 


I 


01 583 


27 


3 


96738 


1-03372 


ll 


34 


98499 


I 


oi524 


26 


4 


96794 


i-o33i2 


35 


98556 


1 


01465 


25 


5 


9 685o 


1-03252 


55 


36 


98613 


I 


01406 


24 


6 


96907 


1-03192 


5 4 


^ 7 


98671 


I 


oi347 


23 


7 


96963 


i-o3i32 


53 


38 


98728 


I 


01288 


22 


8 


97020 


1-03072 


52 


3 9 


98786 


I 


01229 


21 


9 


97076 


I-030I2 


5i 


4o 


98843 


I 


01170 


20 


10 


97i33 


I-O2o52 


5o 


4i 


98901 


I 


01112 


19 


ii 


97189 


1-02892 


49 


42 


9 8 9 58 


I 


oio53 


l8 


12 


97246 


1-02832 


48 


43 


99016 


I 


00994 


17 


i3 


97302 


1-02772 


47 


44 


99073 


I 


ooo35 


16 


14 


973D9 


1-02713 


46 


45 


99i3i 


I 


00876 


i5 


i5 


97416 


1-02653 


45 


46 


99189 


I 


00818 


14 


16 


97472 


1-02593 


44 


47 


99247 


I 


00759 


i3 


"7 


97529 


1-02533 


43 


48 


99304 


I 


00701 


12 


18 


97586 


1-02474 


42 


49 


99362 


I 


00642 


11 


19 


97643 


1-02414 


4i 


5o 


99420 


I 


oo583 


10 


20 


97700 


1-02355 


4o 


5i 


99478 


I 


oo525 


9 


21 


97756 


1-02295 


39 


52 


99536 


I 


00467 





22 


97813 


1-02236 


38 


53 


99594 


I 


00408 


7 


23 


97870 


1-02176 


37 


54 


99632 


I 


oo35o 


6 


24 


97927 


1-02117 


36 


55 


99710 


I 


00291 
00233 


5 


25 


97984 


1 -02057 


35 


56 


99768 


I 


4 


26 


98041 


1-01998 


34 


5 7 


99826 


I 


00175 


3 


27 


98098 


1 01939 


33 


58 


99884 


I 


001 16 


2 


28 


9 8i55 


1-01879 


32 


5 9 


99942 


I 


ooo58 


1 


29 


98213 


1-01820 


3i 


60 


Unit. 


Unit. 





3o 


98270 


1-01761 


3o 










r 


Cotang. 


Tangent. 


r 


/ 


Cotang. 


Tangent. 


r 


45° 


4 


5° 


TABLE OF CONST. 


ANTS. 




Base of Napier's system of logarithms — 




5 — 2-718281828459 
'. = 0-434294481903 


Mod. of common syst. of logarithms = com 


. lOg. £ = \ 


Batio of circumference to diameter of a circle — 






log. j 


T = 0-497T49872694 


w 2 = 9-869604401089 


V 


rr= I-772453850906 


Arc of same length as radius — 180 ■ 


T- IT = 10800' 


-7- It = 648000" -f- 7T 






\ = I.758l22632409 




log 


.=3.536273882793 


648000" -7-1T — 206264" '8062470964, . .♦ 


log 


■. = 5-3i4425i33i76 


Tropical year = 365d. 5h. 48m. 47s. -588 = 365c 


I. •24221745c 


>, log. = 2 -56258io 


Sidereal year = 365d. 6h. 9m. 10s. -742 = 365< 


1. -25637433: 


», log. = 2-5625978 


24h. sol. t.=24h. 3m. 56s. • 555335 sid. t.=24h. X 1 


00273791,10 


v. 1-002=0-0011874 


24h. sid. t.=24h. — (3m. 55s. • 90944) sol. t.=24h. X < 


3-9972696,10 


g. 0-997=9-9988126 


British imperial gallon — 277 • 274 cubic inches, . 




..log. = 2-4429091 


Length of sec. pend., in inches, at London, 3 


9-13929; Paris, 39-1285; New 


York, 39 '1285. 






French metre = 3-2808992 English/^ = 39-370- 


^904 inches. 




1 cubic inch of water (bar. 3o inches, Fahr. then 


m. 62 ) = 252-458 Troy grains. 



TABLE IV. 



A TEAVERSE TABLE 



SHOWING THE 



DIFFERENCE OF LATITUDE AND DEPARTURE 



FOR 



DISTANCES BETWEEN 1 AND 100, AND EOK ANGLES TO 
QUAKTEK DEGKEES BETWEEN 1° AND 90°. 



86 




TRAVERSE TABLE. 


Table IV. 


d 


i° 


i° 


1° 


O 


5' 

a 












5' 
p 

3 

? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


I '00 


0-00 


I -00 


0-01 


I -00 


0-01 


1 


2 


2 


00 


0-01 


2 


00 


0-02 


2 


• 00 


o-o3 


2 


3 


3 


00 


0-01 


3 


00 


o-o3 


3 


• 00 


0-04 


3 


4 


4 


00 


0-02 


4 


00 


o-o3 


4 


• 00 


o-o5 


4 


5 


5 


00 


0-02 


5 


00 


0-04 


5 


• 00 


0-07 


5 


6 


6 


00 


o-o3 


6 


00 


o-o5 


6 


• 00 


0-08 


6 


2 


7 


00 


o«o3 


7 


■ 00 


0-06 


7 


• 00 


0-09 


7 


8 


00 


o«o3 


8 


• 00 


0-07 


8 


• 00 


0-10 


8 


9 


9 


00 


o-o4 


9 


• 00 


0-08 


9 


• 00 


0-12 


9 


10 


10 


00 


o«o4 


10 


• 00 


0-09 


10 


• 00 


0'i3 


10 


ii 


ii 


00 


o»o5 


11 


.00 


0-10 


11 


■00 


0'i4 


11 


12 


12 


00 


o-o5 


12 


00 


0-10 


12 


• 00 


o-i6 


12 


i3 


i3 


00 


0-06 


i3 


00 


O'll 


i3 


00 


0-17 


i3 


14 


14 


00 


0-06 


14 


00 


0-12 


14 


00 


0-18 


14 


i5 


i5 


00 


0-07 


i5 


00 


0'i3 


i5 


00 


0'20 


i5 


16 


16 


00 


0-07 


16 


00 


o-i4 


16 


00 


0-21 


16 


17 


17 


00 


0-07 


17 


00 


o-i5 


17 


• 00 


0-22 


n 


10 


18 


00 


0-08 


18 


00 


0-16 


18 


• 00 


0-24 


18 


19 


19 


00 


0-08 


19 


00 


0-17 


19 


• 00 


0-25 


19 


20 


20 


00 


0-09 


20 


00 


0'i7 


20 


00 


0-26 


20 


21 


21 


00 


0*09 


21 


00 


0-18 


21 


• 00 


0'27 


21 


22 


22 


00 


0-10 


22 


00 


0-19 


22 


■ 00 


0-29 


22 


23 


23 


00 


0-10 


23 


00 


0-20 


23 


00 


o-3o 


23 


24 


24 


00 


0-10 


24 


00 


0-21 


24 


00 


o-3i 


24 


25 


25 


00 


O-II 


25 


00 


0-22 


25 


00 


0.33 


25 


26 


26 


00 


O-II 


26 


00 


0-23 


26 


00 


o-34 


26 


27 


27 


00 


0-12 


27 


00 


0-24 


27 


00 


o-35 


27 • 


28 


28 


00 


0-12 


28 


00 


0-24 


28 


00 


0-37 


28 


29 


29 


00 


o-i3 


29 


00 


0-25 


29 


00 


o-38 


29 


3o 


3o 


00 


o-i3 


3o 


00 


0-26 


3c 


00 


0-39 


3o 


3i 


3i 


00 


o-i4 


3i 


00 


0-27 


3i 


00 


0-41 


3i 


32 


32 


00 


o-i4 


32 


00 


0-28 


32 


00 


0-42 


32 


33 


33 


00 


0-14 


33 


00 


0-29 


33 


00 


o-43 


33 


34 


34 


00 


o-i5 


34 


00 


o-3o 


34 


00 


o-45 


34 


35 


35 


00 


o-i5 


35 


00 


o-3i 


35 


00 


0-46 


35 


36 


36 


00 


0-16 


36 


00 


o-3i 


36 


00 


0-47 


36 


3? 


37 


00 


0-16 


37 


00 


0-32 


37 


00 


0-48 


37 


38 


38 


00 


0-17 


38 


00 


0-33 


38 


00 


o-5o 


38 


39 


3 9 


00 


0-17 


3 9 


00 


o-34 


39 


00 


o-5i 


39 


4o 


40 


00 


0-17 


40 


00 


o-35 


4o 


00 


0-52 


4o 


4i 


4i 


00 


0-18 


4i 


00 


o-36 


4i 


00 


o-54 


41 


42 


42 


00 


o-i8 


42 


00 


0-37 


42 


00 


0-55 


42 


43 


43 


00 


0-19 


43 


00 


o-38 


43 


00 


o-56 


43 


44 


44 


00 


0-19 


44 


00 


o-38 


44 


00 


o-58 


44 


45 


45 


00 


0-20 


45- 


00 


0-39 


45 


00 


0-59 


45 | 


46 


46 


00 


0-20 


46- 


00 


o-4o 


46 


00 


o-6o 


46 


47 


47 


00 


0-21 


47- 


00 


o-4i 


47 


00 


0-62 


47 


48 


48 


00 


0-21 


48. 


00 


0'42 


48- 


00 


o-63 


48 ; 


P 


49 


00 


0-21 


4 9 - 


00 


0-43 


49. 


00 


0-64 


49 ' 


5o 


5o-oo 


0-22 


5o'00 


o-44 


5o'00 


o-65 


5o s 


i o 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


«5 




a 

OS 

00 














a 

OS 

BO 












3 


8S 


f° 


89i° 


89 


i° 


B 



Table 


IV. 


TRAVERSE TABLE. 




87 


d 


\ 





h° 


1 





g 


a 

a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


CD 


5i 


5i .00 


0-22 


5i-oo 


0-45 


5i-oo 


0-67 


5i 


52 


52 


00 





23 


52 


00 





45 


52-00 


o-68 


52 


53 


53 


00 





23 


53 


00 





46 


53-oo 


0-69 


53 


54 


54 


00 


O 


24 


54 


00 





47 


54-oo 


0-71 


54 


55 


55 


00 





24 


. 55 


00 





48 


55-oo 


0-72 


55 


56 


56 


00 





24 


56 


00 





49 


56-oo 


0-73 


56 


5t 


5 7 


00 





25 


5 7 


00 





5o 


57-00 


0-75 


5 7 


58 


58 


00 





25 


58 


00 





5i 


57.99 


0-76 


58 


5 9 


5 9 


00 


O 


26 


5 9 


00 





5i 


58.99 


0-77 


5 9 


60 


60 


00 





26 


60 


00 





52 


59.99 


o-79 


60 


61 


61 


00 





27 


61 


00 





53 


60-99 


o-8o 


61 


62 


62 


00 





27 


62 


00 





54 


61 -99 


o-8i 


62 


63 


63 


00 





27 


63 


00 





55 


62-99 


0-82 


63 


64 


64 


00 





28 


64 


00 





56 


63-99 


0-84 


64 


65 


65 


00 





28 


65 


00 





5 7 


64-99 


o-85 


65 


66 


66 


00 





29 


66 


00 





58 


65-99 


o-86 


66 


67 


67 


00 





29 


67 


00 





58 


66-99 


o-88 


67 


68 


68 


00 





3o 


68 


00 





5 9 


67.99 


0-89 


68 


69 


69 


00 





3o 


69 


00 





60 


68-99 


0-90 


69 


70 


70 


00 





3i 


70 


00 





61 


69.99 


0-92 


70 


7i 


7i 


00 





3i 


7i 


00 





62 


70-99 


0-93 


7i 


72 


72 


00 





3i 


72 


00 





63 


71-99 


0-94 


72 


73 


73 


00 





32 


73 


00 





64 


72.99 


0-96 


73 


74 


74 


00 





32 


74 


00 





65 


73-99 


0-97 


H 


7 5 


75 


00 





33 


75 


00 





65 


74-99 


0-98 


^ 


76 


76 


00 





33 


76 


00 





66 


7^-99 


0.99 


76 


77 


77 


00 





34 


77 


00 





67 


76-99 


I-OI 


U 


78 


78 


00 





34 


78 


00 





68 


77.99 


1-02 


78 . 


79 


79 


00 





34 


79 


00 





69 


78-99 


i-o3 


79 


80 


80 


00 





35 


80 


00 





70 


79-99 


i-o5 


80 


81 


81 


00 





35 


81 


00 





7i 


80-99 


1-06 


81 


82 


82 


00 





36 


82 


00 





72 


81 -99 


1-07 


82 


83 


83 


00 





36 


83 


00 





72 


82-99 


1-09 


83 


84 


84 


00 





37 


84 


00 





73 


83-99 


I«IO 


84 


85 


85 


00 





37 


85 


00 





74 


84-99 


I'll 


85 


86 


86 


00 





38 


86 


00 





7 5 


85.99 


i-i3 


86 


87 


■ 87 


00 





38 


87 


00 





76 


86-99 


1 -1-4 


87 


88 


88 


00 





38 


88 


00 





77 


87-99 


1-15 


88 


89 


89 


00 





f9 


89 


00 





78 


88-99 


1-16 


89 ; 


90 


90 


00 





39 


90 


00 





79 


89-99 


1-18 


90 


<}i 


9i 


00 





40 


9 1 


00 





79 


90-99 


I- 19 


9 1 


92 


92 


00 





40 


92 


00 





80 


91-99 


1-20 


9 ? 


<)3 


93 


00 





41 


93 


00 





81 


92-99 


1-22 


93 


94 


94 


00 





41 


94 


00 





82 


9 3 -99 


1-23 


H 


9 5 


9 5 


00 





41 


9 5 


00 





83 


94-99 


1-24 


t 


96 


96 


00 





■42 


96 


00 





84 


95-99 


1-26 


96 


97 


97 


00 





•42 


97 


00 





85 


96.99 


1-27 


9 2 


. 98 


98 


00 





43 . 


98 


00 





86 


97*99 


1-28 


98 


99 


99 


•00 





43 


99 


00 





86 


98-99 


i-3o 


99 


100 


100-00 


o-44 


100-00 


0-87 


99.99 


i-3i 


100 


s 

1 aJ 

w 

s 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


as 

S 


8< 


)f° 


89i° 


89 


*° 



88 






TRAVERSE TABLE. 




Table IV. 


g 


1 





I*° 


H° 


1|° 


U 


p 

s 

p 


















BS 

3" 

s 


CO 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


I -00 


0-02 


I -00 


0-02 


I -00 


o-o3 


I -00 


o-o3 


I 


2 


2 


00 


o-o3 


2 


00 


0-04 


2 


00 


o-o5 


2 


00 


0-06 


2 


3 


3 


00 


o-o5 


3 


00 


0-07 


3 


00 


0-08 


3 


00 


0-09 


3 


4 


4 


00 


0-07 


4 


00 


0-09 


4 


00 


O-IO 


4 


00 


0-12 


4 


5 


5 


00 


0-09 


5 


00 


O-II 


5 


00 


o-i3 


5 


00 


o-i5 


5 


6 


6 


00 


o-io 


6 


00 


0'i3 


6 


00 


0-16 


6 


00 


0-18 


. 6 


7 


7 


00 


0'12 


7 


00 


oi5 


7 


00 


<w8 


7 


00 


0-21 


I 


8 


8 


00 


0-14 


8 


00 


0^7 


8 


00 


0-21 


8 


00 


0-25 


9 


9 


00 


0-16 


9 


00 


0-20 


9 


00 


0-24 


9 


00 


0-28 


9 


10 


10 


00 


0-17 


10 


00 


0-22 


10 


00 


0-26 


10 


00 


o-3i 


10 


ii 


11 


00 


0-19 


11 


00 


0'24 


11 


00 


0-28 


10 


99 


o-34 


11 


12 


12 


00 


0-21 


12 


00 


0-26 


12 


00 


o-3i 


11 


99 


0-37 


12 


i3 


i3 


00 


0-23 


i3 


00 


0.28 


i3 


00 


o-34 


12 


99 


o-4o 


i3 


i4 


14 


00 


0'24 


i4 


00 


o-3i 


14 


00 


0-37 


i3 


99 


o-43 


14 


i5 


i5 


00 


0-26 


i5 


00 


0.33 


14 


99 


0-39 


14 


99 


0-46 


i5 


16 


16 


00 


0.28 


16 


00 


0.35 


i5 


99 


0-42 


i5 


99 


0-49 


16 


17 


n 


00 


o-3o 


n 


00 


0-37 


16 


99 


o-45 


16 


99 


0-52 


\l 


18 


18 


00 


o-3i 


18 


00 


0-39 


17 


99 


o-47 


17 


99 


o-55 


19 


19 


00 


o-33 


19 


00 


o-4i 


18 


99 


o-5o 


18 


99 


o-58 


!9 


20 


20 


00 


o-35 


20 


00 


o-44 


19 


99 


0-52 


*9 


99 


o-6i 


20 


21 


21 


00 


0-37 


21 


00 


0-46 


20 


99 


0-55 


20 


99 


0-64 


21 


22 


22 


00 


o-38 


21 


99 


0-48 


21 


99 


o-58 


21 


99 


0-67 


22 


23 


23 


00 


o-4o 


22 


99 


o-5o 


22 


99 


o-6o 


22 


•99 


0-70 


23 


24 


24 


00 


0-42 


23 


99 


0-52 


23 


99 


o-63 


23 


99 


0-73 


24 


25 


25 


00 


o-44 


24 


99 


0-55 


24 


99 


o-65 


24 


•99 


0-76 


25 


26 


26 


00 


o-45 


25 


99 


0-57 


25 


99 


o-68 


25 


99 


0.79 


26 


3 


2 1 


00 


0-47 


26 


99 


0-59 


26 


99 


0-71 


26 


99 


o-83 


27 


28 


00 


0-49 


27 


99 


o-6i 


27 


99 


0-73 


27 


99 


o-86 


28 


29 


1 9 


00 


o-5i 


28 


99 


o-63 


28 


99 


0-76 


28 


99 


0-89 


29 


3o 


3o 


00 


0-52 


29 


99 


o-65 


29 


99 


0-79 


29 


99 


0-92 


3o 


3i 


3i 


00 


o-54 


3o 


99 


o-68 


3o 


99 


o-8i 


3o 


99 


0-95 


3i 


32 


32 


00 


o-56 


3i 


99 


0-70 


3i 


99 


0-84 


3i 


99 


0-98 


32 


33 


32 


99 


o-58 


32 


99 


072 


32 


99 


o-86 


32 


98 


I'OI 


33 


34 


33 


99 


059 


33 


99 


0-74 


33 


99 


0-89 


33 


98 


i-o4 


34 


35 


34 


99 


o-6i 


34 


99 


0-76 


34 


99 


0-92 


34 


.98 


1-07 


35 


36 


35 


99 


o-63 


35 


99 


0-79 


35 


99 


0-94 


35 


.98 


I-IO 


36 


37 


36 


99 


o-65 


36 


99 


0..81 


36 


99 


0.97 


36 


98 


i-i3 


3 7 


38 


37 


99 


o-66 


37 


99 


a- 83 


3 7 


99 


0-99 


37 


98 


1-16 


38 


3 9 


38 


99 


o-68 


38 


99 


o-85 


38 


99 


1-02 


38 


98 


1-19 


39 


40 


39 


99 


0'7o 


39 


99 


0-87 


39 


99 


i'05 


39 


98 


1-22 


40 


4i 


4o 


99 


0-72 


40 


99 


0-89 


4o 


99 


1-07 


4o 


98 


1-25 


4i 


42 


4i 


99 


0-73 


41 


99 


0-92 


4i 


99 


I-IO 


41 


98 


1-28 


42 


43 


42 


99 


0-75 


42 


99 


0-94 


42 


99 


i-i3 


42 


98 


i-3i 


43 


44 


43 


'99 


0-77 


43 


99 


0-96 


43 


99 


i-i5 


43 


98 


1-34 


44 


45 


44 


99 


0-79. 


44 


99 


0-98 


44 


99 


1. 18 


44 


98 


i-3 7 


45 


46 


45 


99 


o-8o 


45 


99 


1 '00 


45 


99 


1-20 


45 


98 


l-4o 


46 


47 


46 


99 


0-82 


46 


99 


i-o3 


46 


99 


1-23 


46 


98 


i-44 


47 


48 


47 


99 


0-84 


47 


99 


i'o5 


47 


98 


1-26 


47 


98 


i-47 


48 


i 9 


48 


99 


o-86 


48 


99 


1-07 


48 


98 


1-28 


48 


98 


1 -5o 


£9 


5o 


49.99 


0-87 


49-99 


1-09 


49-98 


i-3i 


49-98 


i-53 


5o 


6 



c 

CO 

to 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




a 
a 

Q 


8 


9° 


88 


1° 


88 


h° 


88 


i° 



Table IT. 




TRAVERSE TABLE. 






89 


Distance. 


] 





H° 


n° 


1 


i° 


3 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5r 


5o-99 


0-89 


5o>99 


I-II 


5o- 9 8 


1-34 


5o- 9 8 


i-56 


5i 


52 


5i- 99 


0-91 


5i 


•99 


i-i3 


5i 


.98 


1-36 


5i 


.98 


i.5 9 


52 


53 


52-99 


0-92 


52 


•99 


1. 16 


52 


- 9 8 


l-3 9 


52 


.98 


1-62 


53 


54 


53-99 


0-94 


53 


■99 


i- 18 


53 


.98 


i-4i 


53 


•97 


1-65 


54 


55 


54-99 


0-96 


54 


•99 


1-20 


54 


98 


1-44 


54 


'97 


1-68 


55 


56 


55-99 


0-98 


55 


99 


1-22 


55 


98 


1-47 


55 


97 


1. 71 


56 


57 


56-99 


0-99 


56 


■99 


1-24 


56 


9? 


i-4 9 


56 


97 


i-74 


57 


58 


57.99 


I-OI 


57 


99 


1-27 


57 


98 


1-52 


5 7 


97 


1.77 


58 


5 9 


58-99 


i-o3 


58 


99 


I-2 9 


58 


98 


1-54 


58 


97 


i- 80 


5 9 


6o 


59.99 


i-o5 


5 9 


99 


i-3i 


5 9 


98 


i,5 7 


5 9 


97 


i-83 


60 


6i 


60-99 


i- 06 


60 


99 


1.33 


60 


98 


i-6o 


60 


97 


1.86 


61 


62 


61 -99 


1.08 


61 


99 


1-35 


61 


98 


1-62 


61 


97 


1.89 


62 


63 


62.99 


I-IO 


62 


99 


i-3 7 


62 


98 


1-65 


62 


97 


1.92 


63 


64 


63- 99 


I-I2 


63 


98 


i-4o 


63 


98 


1-68 


63 


97 


i- 9 5 


64 


65 


64-99 


i-i3 


64 


98 


1.42 


64 


98 


1-70 


64 


97 


1-99 


65 


66 


65- 99 


i-i5 


65 


98 


1-44 


65 


98 


i- 7 3 


65 


97 


2-02 


66 


67 


66-99 


1. 17 


66 


98 


1-46 


66 


98 


i. 7 5 


66 


97 


2-o5 


67 


68 


67-99 


i- 19 


67 


98 


1.48 


67 


98 


1.78 


67 


97 


2-08 


68 


69 


68-99 


1-20 


68 


98 


i-5i 


68 


98 


1. 81 


68 


97 


2>II 


69 


70 


69-99 


1-22 


69 


98 


i-53 


69 


98 


i-83 


69 


97 


2-14 


70 


7* 


70-99 


1-24 


70 


98 


1-55 


70 


9? 


1.86 


70 


97 


2-17 


7i 


72 


71-99 


1-26 


7i 


9? 


i-5 7 


7i 


98 


i-88 


7i 


97 


2-20 


72 


73 


72-99 


1-27 


72 


98 


i-5 9 


72 


97 


1. 91 


72 


97 


2-23 


73 


74 


73-99 


I -29 


73 


9* 


i- 61 


73 


97 


i-94 


73 


97 


2-26 


74 


7 5 


74-99 


i-3i 


74 


98 


1.64 


74 


97 


1.96 


74 


97 


2-29 


7 5 


76 


75-99 


1-33 


7 5 


98 


1-66 


75 


97 


1-99 


7 5 


96 


2-32 


76 


77 


76-99 


1-34 


76 


98 


i-68 


76 


97 


2-02 


76 


96 


2-35 


77 


78 


77-99 


1-36 


77- 


98 


1-70 


77 


97 


2- 04 


77 


96 


2-38 


78 


79 


78-99 


1-38 


78. 


98 


1.72 


78 


97 


2-07 


78 


96 


2-41 


2 9 


80 


79-99 


i-4o 


79. 


98 


i. 7 5 


79 


97 


2-09 


79 


96 


2-44 


80 


81 


80-99 


i-4i 


80 • 


98 


1.77 


80 


97 


2-12 


80 


96 


2-47 


81 


82 


81 -99 


i-43 


8i- 


98 


1-79 


81. 


97 


2-l5 


81 


96 


2>5o 


82 


83 


82-99 


i-45 


82- 


98 


i- 81 


82- 


97 


2-17 


82 


96 


2-53 


83 


84 


83-99 


1-47 


83- 


98 


1-83 


83- 


97 


2-20 


83 


96 


2-57 


84 


85 


84-99 


1-48 


84- 


98 


i-85 


84 


97 


2-23 


84 


96 


2-6o 


85 


86 


85-99 


i-5o 


85 


98 


i-88 


85 


97 


2-25 


85 


96 


2-63 


86 


8 1 


86-99 


1-52 


86 


98 


1.90 


86- 


97 


2-28 


86 


96 


2-66 


S 


88 


87-99 


1.54 


87 


98 


1-92 


87. 


97 


2-3o 


ll 


96 


2-69 


89 


88-99 


1.55 


88 


98 


i-94 


88 


97 


2-33 


96 


2-72 


89 


90 


89.99 


1.57 


89. 


98 


1.96 


89 


97 


2-36 


89 


96 


2-75 


90 


9 1 


90-99 


1.59 


90 


9S o 


1.99 


90 


97 


2-38 


90 


9 5 


2.78 


91 


92 


91-99 


i-6i 


9i 


98 


2-01 


9i 


97 


2-4i 


9 1 


96 


2-8l 


92 


93 


92-99 


1-62 


92 


98 


2-o3 


9 l 


97 


2-43 


92 


96 


2-84 


9 3 


94 


93-99 


1-64 


93 


98 


2-05 


9 3- 


97 


2-46 


93 


96 


2-87 


9f 


95 


94-99 


1.66 


94 


98 


2-07 


9 4 


97 


2-49 


94 


96 


2-90 


9 i 


96 


9 5 -99 


1-68 


9 5 


98 


2-09 


9 5 


97 


2-5l 


9 2 


96 


2-94 


96 


97 


96-99 


1-69 


96 


9* 


2-12 


96 


97 


2-54 


96 


9 2 


2-96 


9 l 


98 


97-99 


1-71 


97 


98 


2- 14 


97 


97 


2-57 


97 


9 i 


2-99 


98 


99 


98-98 


i. 7 3 


98 


98 


2-l6 


98 


97 


2.59 


98 


9 5 


3-02 


99 


100 


99.98 


i. 7 5 


99.98 


2-l8 


99-97 


2-62 


99 . 9 5 


3-o5 


100 


a 
£ 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




a 


8< 


)° 


88 


1° 


88 


h° 


88 


i° 



90 




■ 


TRAVERSE TABLE. 




Table IV. 


o 
a 


2 





2i° 


2{-° 


2; 


P 


g 

So' 

p 

3 
O 

$ 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


1 -00 


o-o3 


1 «oo 


o-o4 


I -00 


0-04 


I -00 


o«o5 


I 


2 


2 


00 


0-07 


2 


00 


0-08 


2 


00 


0-09 


2 


00 


O-IO 


2 


3 


3 


00 


0-10 


3 


00 


0-12 


3 


00 


o-i3 


3 


00 


o«i4 


3 


4 


4 


00 


0-14 


4 


00 


0-16 


4 


00 


0-17 


4 


00 


0-19 


4 


5 


5 


00 


0-17 


5 


00 


0-20 


5 


00 


0-22 


4 


99 


0-24 


5 


6 


6 


00 


0-21 


6 


00 


0'24 


5 


99 


0-26 


5 


99 


0-29 


6 


I 


7 


00 


0-24 


6 


99 


0-27 


6 


99 


o-3i 


6 


99 


o-34 


I 


7 


99 


0-28 


7 


99 


o«3i 


I 


99 


o-35 


7 


99 


o-38 


9 


8 


99 


o-3i 


8 


99 


0.35 


99 


0-39 


8 


99 


0-43 


9 


10 


9 


99 


0-35 


9 


99 


0-39 


9 


99 


o-44 


9 


99 


0-48 


10 


ii 


10 


99 


o-38 


10 


99 


0-43 


10 


99 


0-48 


10 


99 


0-53 


11 


12 


11 


99 


0-42 


11 


99 


o-47 


11 


99 


0-52 


11 


99 


o-58 


12 


i3 


12 


99 


o-45 


12 


99 


o-5i 


12 


99 


057 


12 


99 


0-62 


i3 


i4 


i3 


99 


0-49 


i3 


99 


o-55 


i3 


99 


o-6i 


i3 


98 


0-67 


14 


i5 


14 


99 


0-52 


14 


99 


0-59 


14 


99 


o-65 


14 


98 


0-72 


i5 


16 


i5 


99 


o-56 


i5 


99 


o-63 


i5 


99 


0-70 


i5 


98 


0.77 


16 


17 


16 


99 


0-59 


16 


99 


0-67 


16 


9 o 


0-74 


16 


.98 


0-82 


\l 


18 


n 


99 


o-63 


n 


99 


0-71 


n 


98 


0-79 


17 


.98 


o-86 


19 


18 


99 


o-66 


18 


99 


0-75 


18 


9? 


o-83 


18 


.98 


0-91 


19 


20 


19 


99 


0-70 


J 9 


98 


0-79 


J 9 


98 


0-87 


19 


.98 


0-96 


20 


21 


20 


99 


0-73 


20 


9 s , 


0-82 


20 


98 


0-92 


20 


98 


I'OI 


21 


22 


21 


99 


0-77 


21 


9* 


o-86 


21 


98 


0-96 


21 


■97 


1 .'06 


22 


23 


22 


99 


o-8o 


22 


98 


0-90 


22 


98 


1 -00 


22 


■97 


I-IO 


23 


24 


23 


99 


0-84 


23 


98 


0-94 


23 


98 


i-o5 


23 


•97 


i-i5 


24 


25 


24 


98 


0-87 


24 


98 


0-98 


24 


98 


1-09 


24 


•97 


1-20 


25 


26 


25 


98 


0-91 


25 


98 


I-02 


25 


98 


i-i3 


25 


•97 


1-25 


26 


27 


26 


98 


0-94 


26 


98 


I- 06 


26 


97 


i- 18 


26 


•97 


i-3o 


27 


28 


27 


98 


0-98 


27 


98 


I -10 


27 


97 


1-22 


27 


•97 


1-34 


28 


29 


28 


98 


I-OI 


28 


98 


i.-i4 


28 


97 


1-26 


28 


97 


i-3 9 


29 


3o 


29 


98 


i-o5 


29 


98 


1-18 


29 


97 


i-3i 


29 


97 


i-44 


3o 


3i 


3o 


98 


i- 08 


3o 


98 


1-22 


3o 


97 


1-35 


3o 


96 


1-49 


3i 


32 


3i 


98 


I-I2 


3i 


98 


1-26 


3i 


97 


i-4o 


3i 


96 


1-54 


32 


33 


32 


98 


i-i5 


32 


97 


i-3o 


32 


97 


i-44 


32 


96 


1-58 


33 


34 


33 


98 


1-19 


33 


97 


1-33 


33 


97 


1.48 


33 


96 


1-63 


34 


35 


34 


98 


1-22 


34 


97 


i-3 7 


34 


97 


1-53 


34 


96 


1-68 


35 


36 


35 


98 


1-26 


35 


97 


i-4i 


35 


97 


i-5 7 


35 


.96 


i- 7 3 


36 


37 


36 


98 


I-2 9 


36 


97 


1-45 


36 


96 


i- 61 


36 


.96 


1.78 


37 


38 


37 


98 


1.33 


37 


97 


i-4 9 


37 


96 


i-66 


37 


96 


1-82 


38 


3 9 


38 


98 


1-36 


38 


97 


i-53 


38 


96 


1-70 


38 


96 


1.87 


39 


4o 


3 9 


98 


1.40 


39 


97 


i-5 7 


39 


96 


i- 7 5 


39 


9 5 


1-92 


4o 


4i 


4o 


98 


1-43 


4o 


97 


i- 61 


4o 


96 


1-77 


4o 


9 5 


1.97 


41 , 


42 


4i 


97 


1-47 


4i 


97 


1-65 


4i 


96 


1-83 


4i 


9 5 


2'02 


42 


43 


42 


97 


i-5o 


42 


97 


1.69 


42 


96 


1-88 


42 


9 5 


2- 06 


43 


44 


43 


97 


i-54 


43 


97 


i. 7 3 


43 


96 


1-92 


43 


9 5 


2- II 


44 


45 


44 


97 


i-5 7 


44 


97 


1-77 


44 


96 


1.96 


44 


9 5 


2-l6 


45 


46 


45 


97 


i-6i 


45 


96 


i-8i 


45 


96 


2-01 


45 


9 5 


2-21 


46 


47 


46 


97 


i-64 


46 


96 


i-85 


46 


96 


2-o5 


46 


9 5 


2-25 


47 


48 


47 


•97 


i-68 


47 


96 


1-88 


47 


9 5 


2«09 


47 


9 5 


2-3o 


48 


^ 9 


48 


97 


1-71 


48 


96 


1.92 


48 


9 5 


2-14 


48 


94 


2-35 


49 


5o 


49-97 


i-74 


49-9,6 


1.96 


49-95 


2-l8 


49.94 


2- 40 


5o 


1 

01 

'n 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




e 

vt 

OD 

R 


8 


3° 


87 


1° 


87 


1? 


87 


i° 



Table IY. 




TRAVERSE TABLE. 






91 


g 

o 
5 


2° 


2|° 


010 


2 


f° 


tj 

3 
O 
CO 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


50.97 


I.78 


50-96 


2*00 


5o>95 


2-22 


5o-94 


2-45 


5i 


52 


ai-97 


I- 81 


5i -96 


2-04 


5i -93 


2-27 


5i-94 


2-5o 


52 


53 


52-97 


1-85 


52-96 


2-08 


52-95 


2-3l 


52-94 


2-54 


53 


54 


53-97 


1-88 


53.96 


2-12 


53- 9 5 


2-36 


53.94 


2-59 


54 


55 


54-97 


1-92 


54-96 


2-l6 


54-95 


2-40 


54-94 


2-64 


55 


56 


D5-97 


1-95 


55-96 


2-20 


55.95 


2-44 


55-94 


2-69 


56 


57 


56-97 


1-99 


56 -96 


2-24 


56-95 


2-49 


56-93 


2-73 


57 


58 


57-96 


2-02 


57.96 


2-28 


57.94 


2-53 


57-9 3 


2-78 


58 


5 9 


58 -96 


2- 06 


58 - 9 5 


2-32 


58- 9 4 


2.57 


58 - 9 3 


2-83 


5 9 


6o 


59-96 


2-09 


59-95 


2-36 


59-94 


2-62 


59-93 


2-88 


60 


6i 


60-96 


2-l3 


60-95 


2-39 


60-94 


2-66 


60-93 


2-93 


61 


62 


61 -96 


2-l6 


61-95 


2.43 


61-94 


2-70 


61 -93 


2-97 


62 


63 


62-96 


2-20 


62-95 


2-47 


62-94 


2-75 


62-93 


3-02 


63 


64 


63 - 9 6 


2-23 


63- 9 5 


2-5l 


63-94 


2-79 


63 - 9 3 


3-07 


64 


65 


64-96 


2-27 


64.95 


2.55 


64-94 


2-84 


64-93 


3-12 


65 


66 


65-96 


2-3o 


65-95 


2.59 


65- 9 4 


2-88 


65-92 


3.17 


66 


67 


66-96 


2.34 


66-93 


2-63 


66-94 


2-92 


66-92 


3-21 


67 


68 


67-96 


•2-37 


67-95 


2-67 


67-94 


2-97 


67.92 


3.26 


68 


69 


68-96 


2-41 


68 - 9 5 


2-71 


68 - 9 3 


3-oi 


68-92 


3-3i 


69 


70 


69-96 


2-44 


69-95 


2-75 


69-93 


3-o5 


69-92 


3-36 


70 


7i 


70-96 


2.48 


70-95 


2-79 


70-93 


3« 10 


70-92 


3-4i 


7i 


72 


71-96 


2-5l 


71-94 


2-83 


7i- 9 3 


3-i4 


71.92 


3-45 


72 


73 


72-96 


2-55 


72-94 


2-87 


72-93 


3-i8 


72-92 


3-5o 


73 


74 


73- 9 5 


2-58 


73-94 


2-91 


73.93 


3-23 


73-91 


3-55 


74 


75 


74-95 


2-62 


74-94 


2-94 


74-93 


3.27 


74-91 


3.6o 


75 


76 


75-95 


2-65 


75-94 


2-98 


75.93 


3-3i 


75.91 


3-65 


76 


77 


76-90 


2-69 


76-94 


3-02 


76.93 


3-36 


76-91 


3.70 


77 


78 


77- 9 5 


2-72 


77-94 


3-o6 


77- 9 3 


3-40 


77-91 


3-74 


78 


79 


78-95 


2-76 


78-94 


3- 10 


78-92 


3-45 


78-91 


3-79 


79 


80 


7 9 - 9 5 


2-79 


79-94 


3-i4 


79-92 


3.49 


79-91 


3-84 


80 


81 


80-95 


2-83 


80-94 


3-i8 


80-92 


3-53 


80-91 


3.89 


81 


82 


8i- 9 5 


2-86 


81 -94 


3-22 


81-92 


3-58 


81.91 


3.93 


82 


83 


82-95 


2-90 


82-94 


3-26 


82-92 


3-62 


82-90 


3.98 


83 


84 


83 - 9 5 


2-93 


83-94 


3-3o 


83- 9 2 


3-66 


83- 9 o 


4-o3 


84 


85 


84-95 


2-97 


84- 9 3 


3-34 


84-92 


3.71 


84-90 


4-o8 


85 


86 


85- 9 5 


3-oo 


85 . 9 3 


3-38 


83-92 


3. 7 5 


85.90 


4-i3 


86 


87 


86- 9 5 


3-o4 


86 - 9 3 


3-42 


86-92 


3-79 


86-90 


4-17 


87 


88 


87.95 


3-07 


87.93 


3-45 


87-92 


3-84 


87-90 


4-22 


88 


89 


88- 9 5 


3- 11 


88 - 9 3 


3-49 


88-92 


3-88 


88-90 


4-27 


89 


90 


89-95 


3-i4 


89.93 


3-53 


89-91 


3- 9 3 


89-90 


4-32 


90 


9 1 


90-95 


3-i8 


90-93 


3.57 


90-91 


3.97 


90-90 


4-3 7 


9i 


92 


9I-94 


3-21 


9i- 9 3 


3-6i 


91.91 


4-oi 


91-89 


4-4i 


92 


9 3 


92-94 


3-25 


92-9 3 


3-65 


92-91 


4-o6 


92-89 


4.46 


93 


94 


93-94 


3-28 


93.93 


3-6 9 


93-91 


4-io 


9 3-8 9 


4-5i 


H 


9 5 


94-94 


3-32 


94-93 


3.73 


94-91 


4-14 


94-89 


4-56 


95 


96 


95-94 


. 3-35 


95-93 


3-77 


95-91 


4-19 


95-89 


4-6i 


96 


97 


96-94 


3-3 9 


96-93 


3-8i 


96-91 


4-23 


96-89 


4-65 


9 l 


98 


97-94 


3-42 


97-92 


3-85 


97-91 


4-27 


97.89 


4.70 


98 


99 


98-94* 


3-46 


98-92 


3-8 9 


98-91 


4-32 


98-89 


4-7 5 


99 


100 


99.94 


3-49 


99-92 


3- 9 3 


99-91 


4-36 


99-88 


4-8o 


100 




s 
a 

5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




c 

S3 

3 


88° 


87 


1° 


87- 


h° 


m 


l ° \ 



92 






TRAVERSE TABLE. 




Table IV. 


O 

S3' 

3 

n 


3 


3 


*l 


i° 


3i° 


3|° 


s» 

S3 


a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


I -00 


o-o5 


I -00 


0-06 


I '00 


o-o6 


I -00 


0-06 


I 


2 


2-00 


0-10 


2- 


00 


O-II 


2-00 


0-12 


2-00 


o-i3 


2 


3 


3-oo 


0-16 


3- 


00 


0-17 


2-99 


o-i8 


2-99 


0-20 


3 


4 


3-99 


0-21 


3- 


99 


0-23 


3-99 


0-24 


3-99 


0-26 


4 


5 


4-99 


0-26 


4- 


99 


0-28 


4.99 


o-3i 


4-99 


o-33 


5 


6 


5.99 


o-3i 


5- 


99 


o-34 


5-99 


0-37 


5.99 


0.39 


6 


I 


6-99 


0-37 


6- 


99 


o-4o 


6-99 


o-43 


6.99 


0-46 


7 


7-99 


0-42 


7 


99 


o-45 


7-9? 


0.49 


7.98 


0-52 


8 


9 


8.99 


0-47 


8 


99 


o-5i 


8- 9 | 


0-55 


8-98 


0-59 


9 


10 


9-99 


0-52 


9 


98 


0-57 


9.98 


o-6i 


9-98 


0-65 


10 


ii 


10-98 


o-58 


10 


98 


0-62 


10-98 


0-67 


10-98 


0-72 


11 


12 


11-98 


o-63 


11 


98 


o-68 


11-98 


0-73 


n-97 


0-78 


12 


i3 


12-98 


o-68 


12 


9§ 


0-73 


12-98 


o-79 


12-97 


o-85 


i3 


i4 


13-98 


0-73 


i3 


9? 


o-79 
0-85 


i3- 9 7 


o-85 


13.97 


0.92 


14 


i5 


14-98 


0-79 


14 


98 


U-97 


0-92 


U-97 


0-98 


i5 


16 


15.98 


0-84 


i5 


97 


0-91 


15.97 


0-98 


15.97 


i-o5 


16 


12 


16-98 


0-89 


16 


97 


0-96 


16.97 


1.04 


16-96 


1.11 


n 


17-98 


0-94 


n 


97 


1-02 


1.7-97 


I-IO 


17-96 


1. 18 


18 


19 


18-98 


0.99 


18 


97 


1-08 


18-96 


i- 16 


18-96 


1-24 


19 


20 


19-97 


i-o5 


l 9 


97 


i-i3 


19-96 


1-22 


19-96 


i-3i 


20 


21 


20-97 


I'lO 


20 


97 


III 


20-96 


1-28 


20-96 


1.37 


21 


22 


21-97 


i-i5 


21 


96 


21-96 


1-34 


21-95 


1-44 


22 


23 


22-97 


1-20 


22 


96 


i-3o 


22-96 


i-4o 


22-95 


i«5o 


23 


24 


23.97 


1-26 


23 


96 


i-36 


23-96 


1-47 


23-95 


1.57 


24 


25 


24-97 


i-3i 


24 


96 


1.42 


24.95 


1-53 


24-95 


1-64 


25 


26 


25-96 


i-36 


25 


96 


1-47 


25-95 


I.59 


25-94 


1-70 


26 


3 


26-96 


1 -41 


26 


96 


1-53 


26-95 


1-65 


26-94 


1.77 


27 


27-96 


1-47 


27 


9 5 


1.59 


27- 9 5 


1. 71 


27.94 


1-83 


28 


o 9 


28-96 


1-52 


28 


^ 


1-64 


28- 9 5 


1.77 


28-94 


.1.90 


2 9 


3o 


29-96 


1.57 


29 


9 5 


1-70 


29-94 


1-83 


29.94 


1-96 


3o 


3i 


30-96 


1.62 


3o 


9 5 


1.76 


3o-94 


1.89 


30.93 


2-o3 


3i 


32 


31-96 


.1-67 


3i 


9 5 


i-8i 


31-94 


1.93 


3i>93 


2.09 


32 


33 


32-95 


i- 7 3 


32 


9 5 


1-87 


32-94 


2-01 


32-93 


2«IO 


33 


34 


33- 9 5 


1.78 


33 


9 5 


i- 9 3 


33-94 


2-08 


33.93 


2-22 


34 


35 


34-95 


1-83 


34 


94 


1.98 


34-93 


2-14 


34.92 


2-29 


35 


36 


35- 9 5 


1-88 


35 


94 


2-04 


35- 9 3 


2-20 


35.92 


2-35 


36 


sz 


36- 9 5 


1-94 


36 


94 


2-10 


36- 9 3 


2-26 


36-92 


2-42 


a 


37.95 


1.99 


37 


94 


2-l5 


37-93 


2-32 


37.92 


2 -40 


39 


38- 9 5 


2-04 


38 


94 


2-21 


38- 9 3 


2-38 


38- 9 2 


2-55 


39 


4o 


39-95 


2-09 


39 


■94 


2-27 


39-93 


2-44 


3 9 . 9 i 


2-62 


40 


4i 


40-94 


2'l5 


4o 


- 9 3 


2-32 


40-92 


2-5o 


40-91 


2-68 


41 


42 


41-94 


2-20 


4i 


- 9 3 


2-38 


41-92 


2-56 


41-91 


2.75 


42 


43 


42-94 


2-25 


42 


- 9 3 


2-44 


42-92 


2-63 


42-91 


2-8l 


43 


44 


43-94 


2-3o 


43 


• 9 3 


2-49 


43-92 


2-69 


43-91 


2-88 


44 


45 


44.94 


2-36 


44 


- 9 3 


2-55 


44-92 


2-76 


44.90 


2-94 


45 


46 


45-94 


2-41 


45 


- 9 3 


2-6l 


45-91 


2-8l 


45-90 


3-oi 


46 


47 


46-94 


2-46 


46 


.92 


2-66 


46-91 


2-87 


46-90 


3.07 


% 


48 


47 -9 3 


2-5l 


47 


• 92 


2-72 


47-91 


2-93 


47-9° 


3-i4 


i? 


48-93 


2-56 


48 


•92 


2-78 


48-91 


2-99 


48-90 


• 3* 20 


49 


5o 


49.93 


2-62 


49-92 


2-83 


49 -9 1 


3-o5 


49.89 


3*27 


5o 


Distance. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


d 

a 

s 


8 


7° 


86 


1° 


86£° 


86 


i° 



Table IV. 




TRAVERSE TABLE. 






93 


g 

ST 

P 

3 


3 





n 





3|° 


3|° 


p 

3 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


5093 


2-67 


5o-92 


2-8 9 


50-90 


3- II 


5o-89 


3-34 


5i 


52 


5i -93 


2-72 


5i 


92 


2 


9 5 


5i 


90 


3 


17 


5i 


° 9 


3 


4o 


52 


53 


52-93 


2-77 


52 


9 1 


3 


00 


52 


90 


3 


24 


52 


89 


3 


47 


53 


54 


53.93 


2-83 


53 


9 1 


3 


06 


53 


90 


3 


3o 


53 


88 


3 


53 


54 


55 


54-92 


2-88 


54 


9 1 


3 


12 


54 


90 


3 


36 


54 


88 


3 


60 


55 


56 


55-92 


2-93 


55 


9 1 


3 


17 


55 


90 


3 


42 


55 


88 


3 


66 


56 


5 7 


56-92 


2-98 


56 


9 1 


3 


23 


56 


89 


3 


48 


56 


88 


3 


73 


5 7 


58 


57-92 


3-o4 


57 


9 1 


3 


29 


57 


89 


3 


54 


57 


88 


3 


79 


58 


5 9 


58- 9 2 


3-09 


58 


9 1 


3 


34 


58 


89 


3 


60 


58 


87 


3 


86 


5 9 


6o 


59-92 


3-i4 


5 9 


90 


3 


4o 


5 9 


89 


3 


66 


5 9 


87 


3 


92 


60 


6i 


60-92 


3-19 


60 


90 


3 


46 


60 


89 


3 


72 


60 


87 


3 


99 


61 


62 


61-92 


3-24 


61 


90 


3 


5i 


61 


88 


3 


79 


61 


87 


4 


o5 


62 


63 


62-91 


3-3o 


62 


90 


3 


5 7 


62 


88 


3 


85 


62 


87 


4 


12 


63 


64 


63-91 


3-35 


63 


90 


3 


63 


63 


88 


3 


9 1 


63 


86 


4 


l 9 


64 


65 


64-91 


3-4o 


64 


90 


3 


69 


64 


88 


3 


97 


64 


86 


4 


25 


65 


66 


65-91 


3-45 


65 


89 


3 


74 


65 


88 


4 


o3 


65 


86 


4 


32 


66 


67 


66-91 


3-5i 


66 


89 


3 


80 


66 


88 


4 


09 


66 


86 


4 


38 


67 


68 


67-91 


3-56 


67 


89 


3 


86 


67 


87 


4 


16 


67 


85 


4 


45 


68 


69 


68-91 


3-6i 


68 


89 


3 


9 1 


68 


87 


4 


21 


68 


85 


4 


5i 


69 


70 


69-90 


3-66 


69 


89 


3 


97 


69 


87 


4 


27 


69 


85 


4 


58 


70 


71 


70-90 


3-72 


70 


89 


4 


o3 


70 


87 


4 


33 


70 


85 


4 


64 


7i 


72 


71-90 


3-77 


7i 


88 


4 


08 


7i 


87 


4 


40 


7i 


85 


4 


7i 


72 


73 


72-90 


3-82 


72 


88 


4 


14 


72 


86 


4 


46 


72 


84 


4 


V 


73 


74 


73-90 


3-8 7 


73 


88 


4 


20 


73 


86 


4 


52 


73 


84 


4 


84 


74 


7 5 


74-90 


3- 9 3 


74 


88 


4 


25 


74 


86 


4 


58 


74 


84 


4 


9 1 


7 5 


76 


75-90 


3- 9 8 


75 


88 


4 


3i 


75 


86 


4 


64 


75 


84 


4 


97 


76 


77 


76-89 


4-o3 


76 


88 


4 


37 


76 


86 


4 


70 


76 


84 


5 


04 


77 


78 


77.89 


4-o8 


77 


87 


4 


42 


77 


85 


4 


76 


77 


83 


5 


10 


78 


79 


78-89 


4-i3 


78 


87 


4 


48 


78 


85 


4 


82 


78 


83 


5 


17 


I 9 


80 


79-89 


4-19 


79 


87 


4 


54 


79 


85 


4 


88 


79 


83 


5 


23 


80 


81 


80-89 


4.24 


80 


87 


4 


5 9 


80 


85 


4 


94 


80 


83 


5 


3o 


81 


82 


81-89 


4-29 


8i- 


87 


4 


65 


81 


85 


5 


01 


81 


82 


5 


36 


82 


83 


82-89 


4-34 


82 


87 


4 


7 1 


82 


85 


5 


07 


82 


82 


5 


43 


83 


84 


83-88 


4.40 


83 


86 


4 


76 


83 


84 


5 


i3 


83 


82 


5 


49 


84 


85 


84-88 


4-45 


84 


86 


4 


82 


84 


84 


5 


19 


84 


82 


5 


56 


85 


86 


85-88 


4-5o 


85 


86 


4 


88 


85 


84 


5 


23 


85 


82 


5 


62 


86 


87 


86-88 


4-55 


86 


86 


4 


93 


86 


84 


5 


3i 


86 


81 


5 


69 


87 


88 


87-88 


4-6i 


87 


86 


4 


99 


87 


84 


5 


37 


87 


81 


5 


76 


88 


89 


88-88 


4-66 


88 


86 


5 


o5 


88 


83 


5 


43 


88 


81 


5 


82 


89 


90 


89-88 


4-71 


89 


86 


5 


10 


89 


83 


5 


49 


89 


81 


5 


89 


90 


9 1 


90-88 


4-76 


90 


85 


5 


16 


90 


83 


5 


56 


90 


81 


5 


9 5 


9 1 


92 


91-87 


4-8i 


9 1 


85 


5 


22 


.9* 


83 


5 


62 


9i 


80 


6 


02 


92 


9 3 


92-87 


4-8 7 


92 


85 


5 


27 


92 


83' 


5 


68 


92 


80 


6 


08 


93 


94 


93-87 


4-92 


9 3 


85 


5 


33 


9 3 


82 


5 


74 


9 3 


80 


6 


i5 


9 i 


9 5 


94-87 


4-97 


94 


85 


5 


39 


94 


82 


5 


80 


94 


80 


6 


21 


9 l 


96 


95-87 


5-02 


9 5 


85 


5 


44 


9 5 


82 


5 


86 


9 3 


79 


6 


28 


96 


97 


96-87 


5-o8 


96 


84 


5 


5o 


96 


82 


5 


9 l 


96 


79 


6 


34 


9 l 


98 


97.87 


5-i3 


97 


84 


5 


56 


97 


82 


5 


98 


■97 


79 


6 


41 


98 


99 


98-86 


5-i8 


98 


• 84 


5 


■ 61 


98 


82 


6 


04 


98 


79 


6 


47 


99 


100 


99-86 


5-23 


99-84 


5-67 


99-81 


6-10 


99-79 


6-04 


100 


4> 
O 

a 
a 

m 

3 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


a 

GO 

5 


8' 


7° 


86 


1° 


86 


i° 


86 


i° 



94 






TRAVERSE TABLE. 




Table IV. 


g 

a 
? 


4 





44° 


H° 


4|° 


O 

5* 

3 
a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


I -00 


0-07 


I '00 


0-07 


I -00 


0-08 


I -00 


0-08 


I 


2 


2 


00 


0-14 


I 


99 


o-i5 


1 


99 


0-16 


1 


99 


0-17 


2 


3 


2 


99 


0-21 


2 


99 


0-22 


2 


99 


0-24 


2 


99 


0-25 


3 


4 


3- 


99 


0-28 


3 


99 


o-3o 


3 


99 


o-3i 


3 


98 


o-33 


4 


5 


4 


99 


0-35 


4 


99 


0-37 


4 


98 


0-39 


4 


98 


o-4i 


5 


6 


5 


99 


0-42 


5 


98 


o-44 


5 


98 


0-47 


5 


98 


o-5o 


6 


7 


6 


98 


0-49 


6 


98 


0-52 


6 


98 


o-55 


6 


97 


o-58 


7 


8 


7 


98 


o-56 


7 


98 


0-59 


7 


98 


o-63 


7 


97 


o-66 


8 


9 


8 


9 ^ 


o-63 


8 


98 


0-67 


8 


97 


0-71 


8 


97 


0-75 


9 


10 


9 


98 


0-70 


9 


97 


0-74 


9 


97 


0-78 


9 


97 


o-83 


10 


ii 


10 


97 


0.77 


10 


97 


0-82 


10 


97 


0-86 


10 


96 


0-91 


11 


12 


11 


97 


o-84 


11 


97 


0.89 


11 


96 


0-94 


11 


96 


0-99 


12 


i3 


12 


97 


0-91 


12 


96 


0-96 


12 


96 


1-02 


12 


96 


I- 08 


i3 


14 


i3 


97 


0-98 


i3 


96 


1- 04 


i3 


96 


1-10 


i3 


9 5 


I- 16 


i4 


i5 


14 


96 


i-o5 


14 


96 


I'll 


14 


9 5 


i-i8 


14 


9 5 


1-24 


i5 


16 


ID 


96 


1 12 


15 


96 


1.19 


i5 


9 5 


1-26 


i5 


9 5 


1-32 


16 


17 


16 


96 


I- 19 


16 


9 5 


1-26 


16 


9 5 


1-33 


16 


94 


1 -4i 


17 


18 


J I 


96 


1-26 


H 


9 5 


1.33 


n 


94 


1 .41 


n 


94 


1-49 


18 


*9 


18 


9 5 


1-33 


18 


q5 


1 -4o 


18 


94 


1-49 


18 


93 


1-57 


19 


20 


19 


9 5 


1-40 


19 


9 5 


1-48 


19 


9 4 


i.5 7 


19 


93 


1-66 


20 


21 


20 


9 5 


1.46 


20 


94 


i-56 


20 


94 


1-65 


20 


93 


i-74 


21 


22 


21 


9 5 


1-53 


21 


94 


1-63 


21 


93 


i- 7 3 


21 


9 2 


1-82 


22 


23 


22 


94 


i-6o 


22 


94 


1-70 


22 


93 


i-8o 


22 


92 


1-90 


23 


24 


23 


94 


1.67 


23 


93 


1-78 


23 


9 3 


i-88 


23 


■92 


1-99 


24 


25 


24 


94 


i-74 


24 


93 


1-85 


24 


92 


1-96 


24 


91 


2-07 


25 


26 


25 


94 


1. 81 


23 


93 


1 -93 


25 


92 


2-04 


25 


9 1 


2-l5 


26 


27 


26 


93 


i-88 


26 


93 


2-00 


26 


92 


2-12 


26 


9 1 


2-24 


27 


28 


27 


93 


i- 9 5 


27 


92 


2-08 


2 1 


9i 


2- 20 


27 


90 


2-32 


28 


29 


28 


93 


2-02 


28 


92 


2-l5 


28 


9i 


2-28 


28 


90 


2-40 


29 


3o 


29 


93 


2 «09 


29 


92 


2-22 


29 


9i 


2-35 


29 


90 


2-48 


3o 


3i 


3o 


92 


2-l6 


3o 


9 1 


2-3o 


3o 


90 


2-43 


3o 


89 


2-57 


3i 


32 


3i 


92 


2-23 


3i 


9i 


2-37 


3i 


90 


2-5l 


3i 


89 


2-65 


32 


33 


32 


92 


2-3o 


32 


9 1 


2-45 


32 


90 


2-59 


32 


89 


2-73 


33 


34 


33 


92 


2-37 


33 


9 1 


2-52 


33 


9° 


2-67 


33 


88 


2-82 


34 


35 


34 


9 1 


2-44 


34 


90 


2-59 


34 


89 


2-75 


34 


88 


2-90 


35 


36 


35 


9 1 


2-5l 


35 


90 


2-67 


35 


89 


2-82 


35 


• 88 


2- 9 8 


36 


37 


36 


9 1 


2-58 


36 


90 


2-74 


36 


89 


2-90 


36 


•87 


3-06 


37 


38 


37 


9* 


2-65 


37 


9° 


2-82 


37 


88 


2-98 


37 


•87 


3-i5 


38 


3 9 


38 


90 


2-72 


38 


89 


2.89 


38 


88 


3-o6 


38 


■87 


3-23 


3 9 


40 


3 9 


90 


2-79 


3 9 


89 


2-96 


3 9 


88 


3-14 


39 


-86 


3-3i 


40 


41 


4o 


90 


2-86 


40 


89 


3.04 


4o 


87 


3-22 


4o 


86 


3-40 


4i 


42 


4i 


90 


2-93 


4i 


88 


3. II 


4i 


87 


3-3o 


41 


86 


3-48 


42 


43 


42 


90 


3-oo 


42 


88 


3-19 


42 


87 


3.37 


42 


85 


3-56 


43 


44 


43 


89 


3-07 


43 


88 


3-26 


43 


86 


3-45 


43 


85 


3-64 


44 


45 


44 


89 


3-i4 


44 


.88 


3-33 


44 


86 


3-53 


44 


85 


3-73 


45 


46 


45 


89 


3-21 


45 


•87 


3-4i 


45 


86 


3-6i 


45 


84 


3.8i 


46 


47 


46 


89 


3-28 


46 


•87 


3.48 


46 


86 


3-6 9 


46 


84 


3-8 9 


47 


48 


47 


88 


3-35 


47 


•87 


3-56 


47 


85 


3-77 


47 


84 


3-97 


48 


49 


48 


88 


3-42 


48 


■87 


3-63 


48 


85 


3-84 


48 


83 


4-o6 


49 


5o 


49-88 


3-49 


49-86 


3.71 


49-85 


3-92 


49-83 


4-i4 


5o 


Distance. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


d 
u 

c 

Q 


8 


6° 


85 


10 
4 


85 


h° 


85 


10 



Table IV. 




TRAVERSE TABLE. 






95 


? 


4 





4i 


3 


4i° 


4| 





b 

re 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


5o-88 


3-56 


5o-86 


3.78 


5o-84 


4-00 


5o-82 


4-22 


5i 


52 


31-87 


3-63 


5i-86 


3- 


85 


5 1. '84 


4- 


08 


5i- 


82 


4 


3i 


52 


53 


52-8 7 


3.70 


52-85 


3- 


9 3 


52-84 


4- 


16 


52- 


82 


4 


39 


53 


54 


53-8 7 


3.77 


53-85 


4- 


00 


53-83 


4- 


24 


53- 


81 


4 


47 


54 


55 


54-87 


3-84 


54-85 


4- 


08 


54-83 


4- 


32 


54- 


81 


4 


55 


55 


56 


55-86 


3.91 


55-85 


4- 


i5 


55-83 


4- 


39 


55- 


81 


4 


64 


56 


57 


56-86 


3.98 


56-84 


4- 


22 


56-82 


4- 


47 


56 


80 


4 


72 


5 7 


58 


57-86 


4-o5 


5 7 -84 


4- 


3o 


57-82 


4 


55 


5 7 


80 


4 


80 


58 


5 9 


58-86 


4-12 


58-84 


4- 


37 


58-82 


4 


63 


58 


80 


4 


89 


5 9 


60 


5 9 -85 


4-19 


5 9 -84 


4- 


45 


59-82 


4 


7i 


5 9 


79 


4 


97 


60 


61 


60 -85 


4-26 


6o- 83 


4- 


52 


6o-8i 


4 


79 


60 


79 


5 


o5 


61 


62 


6i-85 


4-32 


6i- 83 


4- 


5 9 


6i- 81 


4 


86 


61 


79 


5 


i3 


62 


63 


62-85 


4-3 9 


62-83 


4- 


67 


62-81 


4 


94 


62 


78 


5 


22 


63 


64 


63-84 


4.46 


63-82 


4- 


74 


63- 80 


5 


02 


63 


78 


5 


3o 


64 


65 


64-84 


4-53 


64-82 


4- 


82 


64-80 


5 


10 


64 


78 


5 


38 


65 


66 


65-84 


4-6o 


65-82 


4- 


89 


65- 80 


5 


18 


65 


77 


5 


47 


66 


67 


66-84 


4-67 


66-82 


4 


97 


66.79 


5 


26 


66 


77 


5 


55 


67 


68 


67-83 


4-74 


67-81 


5 


04 


67-79 


5 


34 


67 


77 


5 


63 


68 


69 


68-83 


4-8i 


68-8i 


5 


11 


68.79 


5 


4i 


68 


76 


5 


71 


69 


70 ' 


69-83 


4-88 


69-81 


5 


19 


69.78 


5 


49 


69 


76. 


5 


80 


70 


7i 


70-83 


4-95 


70-80 


5 


26 


70.78 


5 


5 7 


70 


76 


5 


• 88 


7. 


72 


71-82 


5-02 


71-80 


5 


34 


71.78 


5 


65 


7i 


73 


5 


.96 


72 


73 


72-82 


5.09 


72-80 


5 


4i 


72.77 


5 


73 


72 


7 5 


6 


04 


73 


74 


73-82 


5.16 


73-8o 


5 


48 


.73-77 


5 


81 


73 


7 5 


6 


•i3 


74 


75 


74-82 


5-23 


74-79 


5 


56 


74-77 


5 


88 


74 


74 


6 


•21 


75 


76 


75-8i 


5-3o 


75-79 


5 


63 


75.77 


5 


96 


75 


74 


6 


•29 


76 


77 


76-81 


5.37 


76-79 


5 


7i 


76-76 


6 


04 


76 


74 


6 


• 38 


11 


78 


77-81 


5-44 


77-79 


5 


78 


77-76 


6 


12 


77 


73 


6 


.46 


78 


79 


78-81 


5-5i 


78-78 


5 


85 


78-76 


6 


20 


78 


• 7 3 


6 


•54 


79 


80 


79.81 


5-58 


79.78 


5 


9 3 


79.75 


6 


28 


79 


• 7 3 


6 


.62 


80 


81 


8o-8o 


5-65 


80-78 


6 


00 


80-75 


6 


36 


80 


72 


6 


•7i 


81 


82 


8i-8o 


5.72 


81-78 


6 


08 


8i- 7 5 


6 


• 43 


81 


• 72 


6 


•79 


82 


83 


82-80 


5.79 


82-77 


6 


i5 


82-74 


6 


5i 


82 


•7i 


6 


•87 


83 


84 


83- 80 


5-86 


83.77 


6 


23 


83-74 


6 


-5 9 


83 


•7i 


6 


.96 


84 


85 


84-79 


5- 9 3 


84-77 


6 


3o 


84.74 


6 


.67 


84 


•7i 


7 


.04 


85 


86 


85.79 


6-oo 


83-76 


6 


37 


85-73 


6 


• 7 5 


85 


•70 


7 


•12 


86 


87 


86-79 


6-07 


86-76 


6 


45 


86- 7 3 


6 


■ 83 


86 


•70 


7 


•20 


87 


88 


87.79 


6-U 


87-76 


6 


52 


87-73 


6 


• 90 


87 


•70 


7 


•29 


88 


89 


88-78 


6-21 


88-76 


6 


60 


88-73 


6 


.98 


88 


.70 


7 


•3 7 


89 


90 


89.78 


6-28 


89.75 


6 


67 


89-72 


7 


• 06 


89 


.69 


7 


•45 


90 


9* 


90-78 


6-35 


90.75 


6 


74 


90-72 


7 


•14 


90 


•69 


7 


•54 


9i 


92 


91.78 


6-42 


91-73 


6 


82 


91.72 


7 


• 22 


9i 


• 68 


7 


•62 


92 


9 3 


92-77 


6-49 


92-74 


6 


89 


92-71 


7 


• 3o 


92 


• 68 


7 


.70 


93 


94 


93-77 


6-56 


9 3 -74 


6 


97 


93.71 


7 


• 38 


93 


• 68 


7 


.78 


9 4 


9 5 


94-77 


6-63 


94-74 


7 


■04 


94-71 


7 


•45 


94 


.67 


7 


•87 


9 5 


96 


93-77 


6-70 


9 5 -74 


7 


• 11 


93-70 


7 


• 53 


93 


.67 


7 


• 9 5 


96 


97 


96-76 


6-77 


96-73 


7 


•19 


96-70 


7 


• 61 


96 


.67 


8 


•o3 


91 


98 


97-76 


6-84 


97-73 


7 


•26 


97.70 


7 


.69 


97 


• 66 


8 


•12 


98 


99 


98-76 


6-91 


98-73 


7 


•34 


98-69 


7 


•77 


98 


• 66 


8 


•20 


99 


100 


99-76 


6-98 


99-73 


7-4i 


99.69 


7-85 


99-66 


8-28 


100 




c 

1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




a 

d 


8 


6° 


85 


1° 


S5h° 


85 


i° 


s 



96 






TRAVERSE TABLE. 




Table IV. 


ST 

P 

a 

/ ? 


5 





5- 


f° 


H° 


5; 


1° 


s 

3 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


I -00 


0-09 


1 -00 


0-09 


I -00 


0«I0 


O.99 


0- 10 


I 


2 


I 


99 


0-17 


I 


99 


0-18 


I 


99 


0-19 


I 


99 


0-20 


2 


3 


2 


99 


0-26 


2 


99 


0-27 


2 


99 


0-29 


2 


98 


o-3o 


3 


4 


3 


98 


o-35 


3 


98 


0-37 


3 


98 


o-38 


3 


98 


o-4o 


4 


5 


4 


98 


o-44 


4 


98 


0-46 


4 


98 


0-48 


4 


97 


o-5o 


5 


6 


5 


98 


0-52 


5 


97 


o-55 


5 


97 


o-58 


5 


97 


o-6o 


6 


7 


6 


97 


o-6i 


6 


97 


0-64 


6 


97 


0-67 


6 


96 


0-70 


7 


8 


7 


97 


0-70 


7 


97 


0-73 


7 


96 


076 


7 


96 


o-8o 


8 


9 


8 


97 


0-78 


8 


96 


0-82 


8 


9£ 


o-86 


8 


9 i 


0-90 


9 


10 


9 


9 6 


0-87 


9 


96 


0-92 


9 


9 5 


0-96 


9 


9 5 


I -00 


10 


ii 


10 


96 


0-96 


10 


9 5 


1-01 


10 


9 5 


i-o5 


10 


94 


I-IO 


11 


12 


11 


9 5 


i-o5 


11 


9 5 


I-IO 


11 


94 


i-i5 


II 


94 


1-20 


12 


i3 


12 


9 5 


i-i3 


12 


9 5 


1. 19 


12 


94 


1-25 


12 


93 


i-3o 


i3 


U 


i3 


9 5 


1-22 


i3 


94 


1.28 


i3 


94 


i-34 


13 


93 


i-4o 


14 


i5 


14 


94 


i-3i 


14 


94 


1.37 


14 


93 


i-44 


14 


92 


i«5o 


i5 


16 


i5 


94 


1-39 


i5 


93 


1-46 


i5 


93 


1-53 


i5 


92 


1 -6o 


16 


n 


16 


94 


1-48 


16 


93 


1-56 


16 


92 


1-63 


16 


9 1 


1-70 


\l 


18 


n 


9 3 


i-5 7 


17 


92 


1-65 


n 


92 


i- 7 3 


17 


9i 


i- 80 


19 


18 


93 


1-66 


18 


92 


1-83 


18 


91 


1-82 


18 


90 


1-90 


19 


20 


19 


92 


i-74 


19 


92 


19 


9 1 


1-92 


19 


90 


2-00 


20 


21 


20 


92 


i-83 


20 


9 1 


1-92 


20 


90 


2-01 


20 


89 


2-10 


21 


22 


21 


92 


1*92 


21 


9i 


2-01 


21 


90 


2-II 


21 


?9 


2- 20 


22 


23 


22 


9 1 


2-00 


22 


90 


2-10 


22 


89 


2-20 


22 


88 


2-3o 


23 


24 


23 


9 1 


2-09 


23 


90 


2-20 


23 


89 


2-3o 


23 


88 


2-4o 


24 


25 


24 


90 


2-l8 


24 


90 


2-29 


24 


88 


2-40 


24 


87 


2-5o 


25 


26 


25 


90 


2-27 


25 


89 


2-38 


25 


88 


2-49 


25 


87 


2- 60 


26 


27 


26 


90 


2-35 


26 


89 


2-47 


26 


88 


2-50 


26 


86 


2-71 


27 


28 


27 


89 


2-44 


27 


88 


2-56 


27 


87 


2-68 


27 


86 


2-8l 


28 


29 


28 


89 


2-53 


28 


88 


2-65 


28 


87 


2-78 


28 


85 


2.91 


^9 


3o 


29 


89 


2-6l 


29 


87 


2-75 


29 


86 


2-88 


29 


85 


3-oi 


3o 


3i 


3o 


88 


2-70 


3o 


87 


2-84 


3o 


86 


2-97 


3o 


84 


3- 11 


3i 


32 


3i 


88 


2-79 


3i 


87 


2-93 


3i 


85 


3-07 


3i 


84 


3-21 


32 


33 


32 


87 


2-88 


32 


86 


3-02 


32 


85 


3-i6 


32 


83 


3-3i 


33 


34 


33 


87 


2-96 


33 


86 


3. II 


33 


84 


3-26 


33 


83 


3-4i 


34 


35 


34 


87 


3-o5 


34 


85 


3-20 


34 


84 


3-35 


34 


82 


3-5i 


35 


36 


35 


86 


3-14 


35 


85 


3-29 


35 


83 


3-45 


35 


82 


3-6i 


36 


37 


36 


86 


3-22 


36 


84 


3.39 


36 


83 


3-55 


36 


81 


3- 7 i 


37 


38 


37 


86 


3-3i 


37 


84 


3-48 


37 


83 


3-64 


37 


81 


3-8i 


38 


3 9 


38 


85 


3.40 


38 


84 


3.57 


38 


82 


3-74 


38 


80 


3.91 


3 9 


4o 


3 9 


85 


3-49 


3 9 


83 


3-66 


3 9 


82 


3-83 


3 9 


80 


• 4-oi 


40 


41 


4o 


84 


3.57 


4o 


83 


3.75 


4o 


81 


3- 9 3 


4o 


79 


4-n 


41 


42 


4i 


84 


3-66 


4i 


82 


3-84 


4i 


81 


4-o3 


4i 


79 


4-21 


42 


43 


42 


84 


3.75 


42 


82 


3- 9 3 


42 


80 


4-12 


42 


78 


4-3i 


43 


44 


43 


83 


3-83 


43 


82 


4-o3 


43 


80 


4-22 


43 


78 


4-4i 


44 


45 


44 


83 


3*92 


44 


81 


4-12 


44 


79 


4-3i 


44 


77 


4-5i 


45 


46 


45 


82 


4-oi 


45 


81 


4-21 


45 


79 


4-4i 


45 


77 


4-6i 


46 


47 


46 


82 


4-io 


46 


80 


4-3o 


46 


78 


4-5o 


46 


76 


4-71 


47 


48 


47 


.82 


4-i8 


47 


80. 


4-3 9 


47 


78 


4-6o 


47 


76 


4-8i 


48 


4 9 


48 


.81 


4-27 


48 


79 


4-48 


48 


77 


4-70 


48 


7 5 


4- 9 i 


P 


5o 


49-81 


4-36 


49-79 


4-58 


49-77 


4-79 


49-75 


5-oi 


5o 



e 
cS 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




a 

a 
a 

m 

S 


8 


5° 


84|° 


84£° 


84i° 



Table 


IV. 




TRAVERSE TABLE. 






97 


B 

m 

3 
a 
a 


5 





H 





H° 


5|° 


3" 
s 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


5o-8i 


4-44 


5o-79 


4-6 7 


5o-77 


4.89 


5o-74 


5. 11 


5i 


52 


5i-8o 


4-53 


51-78 


4-76 


5i- 


76 


4- 


98 


5i- 


74 


5-21 


52 


53 


52-8o 


4-62 


52-78 


4-85 


52- 


76 


5- 


08 


52- 


73 


5-3i 


53 


54 


53.79 


4-7i 


53-77 


4.94 


53- 


75 


5- 


18 


53- 


73 


5-41 


54 


55 


54-79 


4-79 


54-77 


5-o3 


54- 


75 


5- 


27 


54- 


7 2 


5-5i 


55 


56 


55-79 


4-88 


55.77 


5-12 


55- 


74 


5- 


37 


55- 


72 


5-6i 


56 


57 


56-78 


4-97 


56.76 


5-22 


56- 


74 


5- 


46 


56- 


7i 


5.71 


57 


58 


57.78 


5-o6 


57-76 


5-3i 


57- 


73 


5- 


56 


57- 


7i 


5-8i 


58 


59 


58-78 


5-i4 


58-75 


5-4o 


58- 


73 


5- 


65 


58- 


70 


5.91 


59 


6o 


59.77 


5-23 


5 9 - 7 5 


5-49 


5 9 


72 


5- 


75 


5 9 


70 


6-oi 


60 


6i 


60 -77 


5-32 


60-74 


5-58 


6o< 


72 


5- 


85 


60 


69 


6-n 


61 


62 


61-76 


5-4o 


61 -74 


5-67 


6i- 


71 


5- 


94 


6i- 


69 


6-21 


62 


63 


62-76 


5.49 


62-74 


5-76 


62 


71 


6 


04 


62 


68 


6-3i 


63 


64 


63.76 


5-58 


63-73 


5-86 


63 


71 


6 


i3 


63 


68 


6-4i 


64 


65 


64-75 


5-67 


64-73 


5- 9 5 


64 


70 


6 


23 


64 


67 


6-5i 


65 


66 


65-75 


5.75 


65-72 


6-o4 


65 


70 


6 


33 


65 


67 


6-6i 


66 


67 


66-75 


5-84 


66-72 


6-i3 


66 


69 


6 


42 


66 


66 


6.71 


67 


68 


67-74 


5- 9 3 


67-71 


6-22 


67 


69 


6 


52 


67 


66 


6-8i 


68 


69 


68-74 


6-oi 


68-71 


6-3i 


68 


68 


6 


61 


68 


65 


6.91 


69 


70 


69.73 


6-io 


69. 7I 


6.41 


69 


68 


6 


7i 


69 


65 


7-01 


70 


71 


70-73 


6-19 


70-70 


6-5o 


70 


67 


6 


81 


70 


64 


7-n 


71 


72 


71-73 


6-28 


71-70 


6-5 9 


7i 


67 


6 


90 


7i 


64 


7-21 


72 


73 


72-72 


6-36 


72-69 


6-68 


72 


66 


7 


00 


72 


63 


7 -3i 


73 


74 


73-72 


6-45 


7 3-6 9 


6-77 


73 


66 


7 


09 


73 


63 


7-4i 


74 


75 


74-71 


6-54 


74-69 


6-86 


74 


65 


7 


19 


74 


62 


7 -5i 


75 


76 


75.71 


6-62 


75-68 


6- 9 5 


75 


65 


7 


28 


75 


62 


7.61 


76 


77 


76-71 


6-71 


76-68 


7-o5 


76 


65 


7 


38 


76 


61 


7.71 


P 


78 


77.70 


6-8o 


77-67 


7-i4 


77 


64 


7 


48 


77 


61 


7.81 


19 


78-70 


6-89 


78-67 


7-23 


78 


64 


7 


57 


78 


60 


7.91 


V 


.80 


79.70 


6-97 


79-66 


7-32 


79 


63 


7 


67 


79 


60 


8-02 


80 


81 


80-69 


7-06 


8o-66 


7-4i 


80 


-63 


7 


76 


80 


-5 9 


8-12 


81 


82 


81-69 


7-i5 


8i-66 


7-5o 


81 


.62 


7 


86 


81 


■5? 


8-22 


82 


83 


82-68 


7-23 


82-65 


7 -Sg 


82 


62 


7 


96 


82 


• 58 


8-32 


83 


84 


83-68 


7-32 


83-65 


7.69 


83 


•61 


8 


o5 


83 


■ 58 


8.42 


84 


85 


84-68 


7-4i 


84-64 


7.78 


84 


•61 


8 


■ i5 


84 


-5 7 


8-52 


85 


86 


85-67 


7-5o 


85-64 


7.87 


85 


■ 60 


8 


•24 


85 


•57 


8.62 


86 


87 


86-67 


7-58 


86-64 


7.96 


86 


• 6o 


8 


34 


86 


-56 


8-72 


87 


88 


87.67 


7-67 


87 -63 


8-o5 


87 


•5 9 


8 


• 43 


87 


-56 


8-82 


88 


89 


88-66 


7-76 


88-63 


8-U 


88 


-5 9 


8 


• 53 


88 


■ 55 


8-92 


89 


90 


89-66 


7-84 


89-62 


8-24 


89 


-5 9 


8 


• 63 


89 


• 55 


9. 02 


90 


9i 


90-65 


7- 9 3 


90-62 


8-33 


90 


• 58 


8 


.72 


90 


•54 


9. 12 


9i 


92 


91-65 


8-02 


91-61 


8-42 


9 1 


• 58 


8 


.82 


9 1 


•54 


9. 22 


92 


9 3 


92-65 


8-u 


92-61 


8-5i 


92 


•57 


8 


■ 91 


92 


-53 


9-32 


9 3 


94 


9 3- 64 


8-19 


93-6i 


8-6o 


93 


•57 


9 


• 01 


93 


-53 


9-42 


9 4 


9 5 


94-64 


8-28 


94-60 


8-69 


94 


•56 


9 


• 11 


94 


•52 


9-52 


95 


96 


9 5-63 


8-37 


95-60 


8.78 


95 


• 56 


9 


• 20 


9 5 


•52 


9-62 


96 


91 


96- 63 


8-45 


96-59 


8-88 


96 


•55 


9 


-3o 


96 


•5i 


9.72 


91 


98 


97-63 


8-54 


97-59 


8-97 


97 


• 55 


9 


•3 9 


97 


•5i 


9-82 


98 


99 


98-62 


8-63 


98 -5o 


9-06 


98 


•54 


9 


•49 


98 


• 5o 


9.92 


99 


100 


99-62 


8-72 


99-58 


9>i5 


99-54 


9-58 


99. 5o 


10-02 


.100 


a 


3 
3 

m 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




a 

s 


8 


5° 


84 


1° 


84£° 


84 


*° 



98 






TRAVERSE TABLE. 




Table IV. 


g 

65' 



cs 

(D 


6 


D 


6i° 


H° 


6|° 


g 

09 

3 

a 

? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


0-99 


0-10 


0-99 


Oil 


O.99 


O-II 


0-99 


o-I2 


I 


2 


1.99 


0-21 


1-99 


0-22 


I- 


99 


0-23 


1 


99 


0-24 


2 


3 


2-98 


o-3i 


2-98 


o-33 


2 


9§ 


o-34 


2 


98 


o-35 


3 


4 


3.98 


0-41 


3- 9 8 


o-44 


3 


97 


o-45 


3 


97 


0-47 


4 


5 


4-97 


0-52 


4-97 


o-54 


4 


97 


0.57 


4 


97 


0.59 


5 


6 


5-97 


o-63 


5.96 


o-65 


5 


96 


o-68 


5 


96 


0-71 


6 


7 


6-96 


0-73 


6-96 


0-76 


6 


96 


0.79 


6 


9 5 


' 0-82 


7 


8 


7-96 


0-84 


7- 9 5 


0-87 


7 


9 5 


0-91 


7 


94 


0-94 


8 ' 


9 


8- 9 5 


0/94 


8- 9 5 


0-98 


8 


94 


I -02 


8 


94 


1 -o6 


9 


10 


9 . 9 5 


i-o5 


9.94 


1 -09 


9 


94 


i-i3 


9 


9 3 


1-18 


10 


ii 


10-94 


i-i5 


10-93 


1-20 


10 


93 


1-25 


10 


92 


1-29 


11 


12 


11-93 


1-25 


11-93 


i-3i 


11 


92 


i-36 


11 


92 


1. 41 


12 


i3 


12-93 


1-36 


12-92 


1-42 ' 


12 


92 


i-47 


12 


9 1 


i-53 


i3 


14 


i3-92 


1-46 


i3-92 


1-52 


i3 


9i 


1 .59 


i3 


90 


1-65 


14 


i5 


14-92 


i-5 7 


14-91 


1-63 


14 


90 


1 -70 


14 


90 


1-76 


i5 


16 


i5-9i 


1-67 


15-90 


i-74 


i5 


2° 


1. 81 


i5 


°9 


1-88 


16 


17 


16-91 


1.78 


16-90 


i-85 


16 


89 


1.92 


16 


88 


2-00 


17 


18 


17-90 
18.90 


i-88 


17-89 


1-96 


H 


88 


2- o4 


n 


88- 


2-12 


18 


J 9 


1-99 


18-89 


2-07 


18 


88 


2-l5 


18 


87 


2-23 


19 


20 
21 


19-89 


2-09 


19-88 


2-18 


19 


87 


2-26 


19 


86 


2-35 


20 


20-88 


2-20 


20-88 


2-29 


20 


87 


2-38 


20 


85 


2-47 


21 


22 


21-88 


2-3o 


21-87 


2-40 


21 


86 


2-49 


21 


85 


2-59 


22 


23 


22-87 


2-40 


22-86 


2-5o 


22 


85 


2- 60 


22 


84 


2-70 


23 


24 


23-87 


2-DI 


23-86 


5-6l 


23 


85 


2-72 


23 


• 83 


2-82 


24 


25 


24-86 


2-6l 


24-85 


2.72 


24 


84 


2-83 


24 


83 


2-94 


25 


26 


25-86 


2.72 


25-85 


2-83 


25 


83 


2-94 


25 


■82 


3-o6 


26 


27 


26-85 


2-82 


26-84 


2-94 


26 


83 


3-o6 


26 


81 


3.17 


27 


28 


27-85 


2-93 


27-83 


3-o5 


27 


■82 


3-i 7 


27 


•8i 


3-29 


28 


29 


28-84 


3-o3 


28-83 


3- 16 


28 


81 


3-28 


28 


80 


3-4i 


29 


3o 


29-84 


3-14 


29-82 


3-27 


29 


81 


3-4o 


29 


79 


3-53 


3o 


3i 


3o-83 


3-24 


3o-82 


3-3 7 


3o 


80 


3-5i 


3o 


79 


3-64 


3i 


32 


3i-82 


3-34 


3i-8i 


3-48 


3i 


79 


3.62 


3i 


78 


3-76 


32 


33 


32-82 


3-45 


32-8o 


3-5 9 


32 


79 


3-74 


32 


77 


3-88 


33 


34 


33.81 


3-55 


33- 80 


3-70 


33 


78 


3-85 


33 


76 


4-oo 


34 


35 


34-8i 


3-66 


34-79 


3-8i 


34 


78 


3- 9 6 


34 


.76 


4- ii 


35 


36 


35.8o 


3-76 


35.79 


3-92 


35 


77 


4-o8 


35 


•75 


4-23 


36 


37 


36- 80 


3-87 


36.78 


4-o3 


36 


.76 


4-19 


36 


• 7 5 


4-35 


3 7 


38 


37.79 


3-97 


37-77 


4-i4 


37 


.76 


4-3o 


37 


•74 


4-47 


38 


39 


38.79 


4.08 


38-77 


4-25 


38 


•75 


4-4i 


38 


■73 


4-58 


39 


4o 


39.78 


4-i8 


39.76 


4-35 


39 


•74 


4-53 


3 9 


■72 


4.70 


4o 


4i 


40.78 


4-29 


40-76 


4.46 


4o 


•74 


4-64 


4o 


• 72 


4-82 


4i 


42 


4i-77 


4-3 9 


41-75 


4-57 


4i 


■73 


4-76 


4i 


•7i 


4-94 


42 


43 


42-76 


4.49 


42-74 


4-68 


42 


•72 


4-8 7 


42 


■ 70 


5-o5 


43 


44 


43-76 


4-6o 


43.74 


4-79 


43 


•72 


4- 9 8 


43 


.70 


5-17 


44 


45 


44-75 


4-7° 


44-73 


4.90 


44 


•7i 


5-09 


44 


• 69 


5.29 


45 


46 


45-75 


4-8i 


45.73 


5-oi 


45 


•70 


5-21 


45 


•68 


5-4i 


46 


47 


46-74 


4-91 


46-72 


5-12 


46 


.70 


5-32 


46 


.67 


5-52 


47 


48 


47-74 
48-73 


5- 02 


47-71 


5-23 


47 


.69 


5-43 


47 


.67 


5-64 


48 


49 


5-12 


48.71 


5-34 


48 


■69 


5-55 


48 


66 


5-76 


49 


5o 


49-73 


5-23 


49-70 


5-44 


49-68 


5-66 


49-65 


5-88 


5o 


Distance. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


OJ 

a 
B 
(4 
GA 

s 


8 


4° 


83 


30 


83 


h° 


83 


i° 





















I 


Table IV. 




TRAVERSE TABLE. 




99 


i 

j 


g 


6 





6i° 


H° 


6|° 


05 
CD 


I 


CD 


Lat. 


Dep. 


Lat. 


Dep. 


1 

Lat. 


Dep. 


Lat. 


Dep. 




Si 


5o-72 


5-33 


5o-70 


5-55 


5o-67 


5 77 


5o-65 


5.99 


5i 




52 


5i -72 


5-44 


5i-6o 


5 --66 


5i- 


67 


5 


89 


5i 


64 


6- 11 


52 




53 


52-71 


5-54 


52-68 


5.77 


52- 


66 


6 


00 


52 


63 


6-23 


53 




54 


53-70 


5-64 


53-68 


5-88 


53 


65 


6 


11 


53 


63 


6-35 


54 


' 


55 


54-70 


5- 7 5 


54-67 


5-99 


54 


65 


6 


23 


54 


62 


6-46 


55 




56 


55-69 


5-85 • 


55-67 


6>io 


55 


64 


6 


34 


55 


61 


6-58 


56 




3 


56- 69 


5- 9 6 


56-66 


6-21 


56 


63 


6 


45 


56 


60 


6-70 


5 7 




5 7 - 68 


6-o6 


57-66 


6-3i 


57 


63 


6 


5 7 


5 7 


60 


6-82 


58 




59 


58-68 


6-17 


58-65 


6-42 


58 


62 


6 


68 


58 


5 9 


6- 9 3 


5 9 




60 


59-67 


6-27 


5g-64 


6-53 


5 9 


61 


6 


79 


5 9 


58 


7-o5 


60 


I 


61 


60-67 


6-38 


60-64 


6-64 


60 


61 


6 


9 1 


60 


58 


7.17 


61 




62 


6i-66 


6-48 


61 -63 


6-75 


61 


60 


7 


02 


61 


5 7 


7-29 


62 




63 


62-65 


6-59 


62-63 


6-86 


62 


60 


7 


i3 


62 


56 


7-40 


63 




64 


63-65 


6-69 


63-62 


6-97 


63 


5 9 


7 


25 


63 


56 


7-52 


64 




65 


64-64 


6-79 


64-61 


7-08 


64 


58 


7 


36 


64 


55 


7-64 


65 


i 


66 


65-64 


6-90 


65-6i 


7.19 


65 


58 


7 


47 


65 


54 


7-76 


66 




67 


66-63 


7-00 


66- 60 


7-29 


66 


5 7 


7 


58 


66 


54 


7-88 


67 




68 


67-63 


7-n 


67-60 


7-4o 


67 


56 


7 


70 


67 


53 


7.99 


68 




69 


68-62 


7-21 


68- 5 9 


7 -5i 


68 


56 


7 


81 


68 


52 


8-ii 


69 




70 


69-62 


7-32 


69 -58 


7-62 


69 


55 


7 


92 


69 


5i 


8-23 


70 




7i 


70-61 


7-42 


70-58 


7.73 


70 


54 


8 


04 


70 


5i 


8-35 


7 1 jj 




72 


71-61 


7-53 


71-57 


7-84 


7i 


54 


8 


i5 


7i 


5o 


8-46 


7 2 ii 




73 


72-60 


7-63 


72-57 


7.95 


72 


53 


8 


26 


72 


49 


8-58 


73 




74 


73-5 9 


7'74 


73-56 


8-06 


73 


52 


8 


38 


73 


49 


8-70 


74 




7 5 


74- 5o 


7-84 


74-55 


8-17 


74 


52 


8 


49 


74 


48 


8-82 


75 




76 


75-58 


7-94 


75.55 


8-27 


7 5 


5i 


8 


60 


7 5 


47 


8- 9 3 


76 


1 7 2 

;j 78 


76-58 


8-o5 


76-54 


8-38 


76 


5i 


8 


72 


76 


47 


9-o5 


77 


77.57 


8-i5 


77.54 


8-49 


77 


5o 


8 


83 


77 


46 


9.17 


78 


1 79 


78-57 


8-26 


78.53 


8-6o 


78 


49 


8 


94 


78 


45 


9-29 


79 


1 8o 


79-56 


8-36 


79-53 


8-71 


79 


49 


9 


.06 


79 


45 


9-40 


80 | 


1 8l 


8o- 56 


8-47 


8o-52 


8-82 


80 


48 


9 


•17 


80 


44 


9-52 


81 


1 82 


8i-55 


8-5 7 


8i- 5i 


8- 9 3 


81 


47 


9 


28 


81 


43 


9.64 


82 


I 83 


82-55 


8-68 


82-5i 


9-04 


82 


47 


9 


40 


82 


42 


9.76 


83 


i 84 


83-54 


8-78 


83 -5o 


9-14 


83 


46 


9 


• 5i 


83 


42 


9.87 


84 


, 85 


84-53 


8-88 


84 -5o 


9. 25 


84 


•45 


9 


62 


84 


41 


9-99 


85 


J 86 


85-53 


8-99 


85-49 


9-36 


85 


•45 


9 


•74 


85 


40 


10-11 


86 


1 87 


86-52 


9.09 


86-48 


9-47 


86 


•44 


9 


• 85 


86 


40 


10-23 


87 


• 


88 


87.52 


9-20 


87-48 


9-58 


87 


• 43 


9 


96 


87 


3 9 


io-34 


88 


r 


89 


88-5i 


9>3o 


88-47 


9.69 


88 


• 43 


10 


08 


88 


38 


10-46 


89 




90 


8901 


9-4i 


89-47 


9-80 


89 


•42 


10 


• 19 


89 


38 


io- 58 


90 




9 1 


90 -5o 


9>5i 


90-46 


9-91 


90 


•42 


10 


• 3o 


90 


37 


10-70 


91 




92 


9i-5o 


9-62 


9I-45 


10-02 


9 1 


•4i 


10 


•41 


9 1 


36 


io- 81 


92 




9 3 


92-49 


9.72 


92-45 


10-12 


92 


■ 40 


10 


■ 53 


92 


36 


10-93 


93 




94 


93-40 


9-83 


93-44 


10-23 


93 


■40 


10 


64 


93 


35 


11 -o5 


94 




95 


94-48 


9 - 9 3 


94-44 


io-34 


94 


• 3 9 


10 


75 


94 


34 


11-17 


9 5 




96 


95.47 


io-o3 


95-43 


io-45 


9 5 


• 38 


10 


87 


9 5 


33 


11-28 


96 




97 


96-47 


io-i4 


96-42 


io-56 


96 


• 38 


10 


98 


96 


33 


n-4o 


97 




98 


97.46 


10-24 


97.42 


10-67 


97 


• 3 7 


11 


• 09 


97 


32 


11-52 


98 




99 


98-46 


io-35 


98-41 


10-78 


98 


• 36 


11 


• 21 


98 


3i 


n-64 


99 




100 


99-45 


io-45 


99-41 


10-89 


99-36 


11-32 


99.31 


ii- 7 5 


100 







e 

s 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


CO 



S3 

ft 

s 




8 


40 


83|° 


83i° 


83 


*° 












111 !■ mill 1 























i 

r 


100 






TRAVERSE TABLE. 




Table IV. 


o 

& 

p 
a 
a 


7 





u° 


n° 


1%° 


a 


Lat, 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat; 


Dep. 


I 


o 99 


0-12 


0-99 


o-i3 


99, 


o-i3 


99 > 


0-l3 


I 


2 


i 


99 


0-24 


I 


98 


o«25 


I 


98 


0-26 


1 


98 





27 


2 


3 


2 


98 


0-37 


2 


98 


o-38 


2 


97 


0-39 


2 


97 





40 


3 


4 


3 


97 


0-49 


3 


97 


o-5o 


3 


97 


0-52 


3 


96 





54 


4 


1 5 


4 


96 


o-6i 


4 


96 


o-63 


4 


96 


o-65 


4 


9 5 





67 


5 


6 


5 


96 


0-73 


5 


9 5 


0-76 


5 


96 


0-78 


5 


95 





81 


6 


7 


6 


9 5 


o-85 


6 


94 


0.88 


6 


94 


0-91 


6 


94 





94 


I 


8 


7 


94 


o-97 


7 


94 


I-OI 


7 


93 


i- 04 


7 


93 


I 


08 


9 


8 


9? 


I-IO 


8 


93 


I-I4 


8 


92 


i- 17 


8 


9 * 


I 


21 


9 


10 


9 


9 3 


I '2^2 


9 


92 


1-26 


9 


9i 


i-3i 


9 


91 


I 


35 


10 


ii 


10 


92 


i-34 


10 


9i 


1-39 


10 


9i 


1-44 


10 


90 


I 


48 


11 


12 


ii 


9 1 


1-46 


11 


90 


i-5i 


11 


90 


1.57 


11 


89, 


I 


62 


12 


i3 


12 


90 


1-58 


12 


90 


1-64 


12 


89 


1-70 


12 


88 


I 


7 5 


i-3 


U 


i3 


00 


171 


i3 


s? 


1.77 
1.89? 


i3 


88 


1-83 


i3 


87 


I 


89 


14 


i5 


14 


89 


1-83 


14 


14 


87 


1-96 


14 


86- 


2 


02 


i5 


16 


i5 


88 


1-95 


i5 


87 


2- 02 


i5 


86 


2-09 


i5 


85 


2 


16 


16 


13 


16 


87 


2-07 


16 


86 


2'l5 


16 


85 


2-22' 


16 


84 


2 


3 


VI 


17 


87 


2-19 


17 


86 


2-27 


17 


85 


2-35 


17 


84 


2 


18 


J 9 


10 


86 


2-32 


18 


85 


2-40 


18 


84 


2-48 


18 


-83 


2 


■56 


J 9 


20 


19 


85 


2-44 


19 


84 


2-52 


19 


83 


2-6l 


19 


82* 


2 


.70 


20 


21 


20 


84 


2-56 


20 


83 


2-65 


20 


82 


2-74 


20 


81 


2 


•83 


21 


22 


21 


84 


2-68 


21 


82 


2-78 


21 


81 


2-87 


21 


-8o 


2 


•97 


22 


23 


22 


83 


2-80 


22 


82 


2-90 


22 


80 


3-oo 


22 


79. 


3 


-10 


23 


24 


23 


82 


2-92 


23 


81 


3-o3 


23 


79 


3-i3 


23 


• 78 


3 


•24 


24 


25 


24 


81 


3-o5 


24 


80 


3-i5 


24 


79 


3-26 


24 


•77 


3 


•37 


25 


26 


25 


81 


3.17 


2D 


79 


3-28 


25 


78 


3-3 9 


25 


.76 


3 


• 5i 


26 


27 


26 


80 


3-29 


26 


78 


3-4i 


26 


77 


3-52 


26 


75 


3 


64 


27 


28 


27 


7? 


3-4i 


27 


78 


3-53 


27 


76 


3-65 


27 


74 


3 


.78 


28 


29 


28 


78 


3-53 


28 


77 


3-66 


28 


7 5 


3-79 


28 


74 


3 


9 1 


29 


3o 


29 


78 


3-66 


29 


76 


3-79 


29 


74 


3-92 


29 


73 


4 


o5 


3o 


3i 


3o 


77' 


3- 7 8 


3o 


75 


3-91 


3o 


73 


4-o5 


3o 


72 


4 


18 


3i 


32 


3i 


t 


3-90 


3i 


74 


4-o4 


3i 


73 


4-i8 


3i 


7i 


4 


32 


32 


33 


32 


75 


4-02 


32 


74 


4-i6 


32 


72 


4-3i 


32 


70 


4 


45 


33 


34 


33 


75 


4-i4 


33 


73 


4-29 


33 


7i 


4-44 


33 


69 


4 


58 


34 


35 


34 


74 


4-27 


34 


72 


4-42 


34 


70 


4-57 


34 


68 


4 


72 


35 


■ 36 


35 


73 


4-3 9 


35 


7i 


4-54 


35 


69 


4-70 


35 


67 


4 


85 


36 


37 


36 


72 


4-5i 


36 


70 


4-67 


36 


68 


4-83 


36 


• 66 


4 


99 


37 


38 


37 


72 


4-63 


37 


70 


4-8o 


37 


67 


4-96 


37 


65 


5 


12 


38 


3 9 


38 


7i 


4-75 


38 


& 


4-92 


38 


67 


5-09 


38 


64 


5 


26 


3 9 


4o 


3 9 


70 


4-8 7 


3 9 


5-o5 


3 9 


66 


5-22 


39 


63 


5 


39 


4o 


4i 


40 


70 


5-oo 


4o 


67 


5.17 


40 


65 


5.35 


4o 


63 


5 


53 


4i 


42 


41 


69 


5-12 


41 


66 


5-3o 


41 


64 


5-48 


41 


62 


5 


66 


42 


43 


42 


68 


5-24 


42 


66 


5-43 


42 


63 


5-6i 


42 


61 


5 


80 


43 


44 


43 


67 


5-36 


43 


65 


5-55 


43 


62 


5-74 


43 


60 


5 


93 


44 


45 


44 


67 


5.48 


44 


64 


5-68 


44 


62 


5.87 


44 


5o 


6 


07 


45 


46 


45 


66 


5-6i 


45 


63 


5-8i 


45 


61 


6-oo 


45 


58 


6 


20 


'46 


% 


46 


65 


5.73 


46 


62 


5- 9 3 


46 


60 


6-i3 


46 


57 


6 


34 


47 ; 


A l 


•64 


5-85 


47 


62 


6-o6 


47 


5 9 


6-27 


47 


56 


6- 


47 


48 


P 


48 


63 


5.97 


48 


61 


6-i8 


48 


58 


6-40 


48 


55 


6- 


61 


49 ; 


5o 


49-63 


6-09 


49' 60 


6-3i 


49- 5 7 


6-53 


49-54 


6-74 


5o 


6 
e> 

8 
et 

s 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




a 

OB 

O 


8 


3° 


82|° 


82 


h° 


82i° 



Table IV. 




TRAVERSE TABLE. 






101 


u 

s 


7 





n 


O 


n° 


7|° 


g 

3 

a 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


5o-62 


6-22 


5o-5g 


6-44 


5o-56 


6-66 


5o-53 


6-88 


5i 


52 


5i 


61 


6-34 


5i 


58 


6-56 


5i-56 


6-79 


5i-53 


7-01 


52 


53 


52 


60 


6-46 


52 


58 


6-69 


52-55 


6-92 


52-52 


7-i5 


53 


54 


53 


60 


6-58 


53 


57 


6-8i 


53-54 


7-o5 


53-5i 


7.28 


54 


55 


54 


5 9 


6-70 


54 


56 


6-94 


54-53 


7-18 


54-5o 


7.42 


55 


56 


55 


58 


6-82 


55 


55 


7.07 


55-52 


7-3i 


55-40 


7 -55 


56 


5-7 


56 


58 


6- 9 5 


56 


54 


7-19 


56-5i 


7-44 


56-48 


7.69 


57 


58 


57 


57 


7-07 


5 7 


54 


7-32 


57.50 


7.57 


57-47 


7.82 


58 


5 9 


58 


56 


7-19 


58 


53 


7-45 


58 -5o 


7-70 


58-46 


7-96 


5 9 


6o 


5 9 


55 


7-3i 


5 9 


52 


7.57 


59-49 


7-83 


59-45 


8-09 


60 


6i 


60 


55 


7-43 


60 


5i 


7.70 


60-48 


7-96 


6o-44 


8-23 


61 


62 


61 


54 


7-56 


61 


5o 


7-82 


61.47 


8-09 


61 -43 


8-36 


62 


63 


62 


53 


7-68 


62 


5o 


7-95 


62-46 


8-22 


62-42 


8-5o 


63 


64 


63 


52 


7-80 


63 


49 


8-o8 


63-45 


8-35 


63-42 


8-63 


64 


65 


64 


52 


7-92 


64 


48 


8-20 


64-44 


8-48 


64-41 


8.77 


65 


66 


65 


5i 


8-04 


65 


47 


8-33 


65-44 


8-6i 


65-40 


8-90 


66 


6 l 


66 


5o 


8-17 


66 


46 


8-46 


66-43 


8-75 


66-39 


9.04 


67 


68 


67 


49 


8-29 


67 


46 


8-58 


67-42 


8-88 


67-38 


9.17 


68 


69 


68 


49 


8.41 


68 


45 


8-71 


68-41 


9-01 


68-37 


9>3o 


69 


70 


69 


48 


8-53 


69 


44 


8-83 


69-40 


9-i4 


69 -36 


9.44 


70 


7i 


70 


47 


8-65 


70 


43 


8-96 


70-39 


9.27 


70-35 


9.57 


7i 


72 


7i 


46 


8.77 


7i 


42 


9-09 


71-38 


9-40 


71-34 


9-71 


72 


73 


72 


46 


8-90 


72 


42 


9-21 


72-38 


9-53 


72-33 


9-84 


73 


74 


73 


45 


9-02 


73 


41 


9-34 


73.37 


9-66 


73-32 


9-98 


74 


75 


74 


44 


9-14 


74 


4o 


9.46 


74-36 


9-79 


74-3i 


10-11 


75 


76 


75 


43 


9-26 


75 


3 9 


9 -5 9 


75-35 


9-92 


75-3i 


10-25 


76 


3 


76 


43 


9-38 


76 


38 


9.72 


76-34 


io-o5 


76 -3o 


io-38 


77 


77 


42 


9- 5i 


77 


38 


9.84 


77-33 


10. 18 


77.29 


10-52 


78 


Z 9 


78 


4i 


9-63 


78 


37 


9-97 


78-32 


io-3i 


78-28 


10-65 


Z 9 


80 


79 


4o 


9.75 


79 


36 


10-10 


79-32 


10-44 


79.27 


10.79 


80 


81 


80 


4o 


9-87 


80 


35 


10-22 


8o-3i 


10-57 


80-26 


10-92 


81 


82 


81 


3 9 


9.99 


81 


34 


10-35 


8i-3o 


10-70 


8i-25 


11 -06 


82 


83 


82 


38 


10- 12 


82 


34 


10-47 


82-29 


10-83 


82-24 


11-19 


83 


84 


83 


37 


10-24 


83 


33 


io-6o 


83-28 


10-96 


83-23 


n-33 


84 


85 


84 


37 


io-36 


84 


32 


10-73 


84-27 


11-09 


84-22 


n-46 


85 


86 


85 


36 


10-48 


85 


3i 


10-85 


85-26 


11-23 


85-21 


11 -6o 


86 


I 8 7 


86 


35 


10-60 


86 


3o 


10-98 


86-26 


u-36 


86.21 


ii. 7 3 


a 


I 86 


87 


34 


10-72 


87 


3o 


ii-ii 


87-25 


n-49 


87-20 


11-87 


89 


88 


34 


10-85 


88 


29 


11-23 


88-24 


11-62 


88-19 


12-00 


89 


90 


89 


33 


10.97 


89 


28 


n-36 


89- 23 


11.75 


89-18 


12-14 


90 


i 9- 


90 


32 


11-09 


90 


27 


n-48 


90.22 


11.88 


90-17 


12-27 


9 1 


} 92 


9i 


3i 


11*21 


9- 


26 


ii-6i 


91-21 


12-01 


91-16 


12-41 


92 


i 9 3 


92 


3i 


n-33 


92 


26 


u-74 


92-20 


12-14 


92-i5 


12-54 


9 3 


I 94 


93 


3o 


11-46 


93 


25 


n-86 


93-20 


12-27 


93-i4 


12-68 


9 i 


i 95 


94 


' 2 9, 


n-58 


94 


24 


u-99 


94-iq 


12-40 


94-i3 


I2-8l 


95 


S 96 


9 D 


28 


11-70 


9 5 


23 


12-12 


95.18 


12-53 


93-12 


12-95 


96 


I 97 


96 


28 


11-82 


96 


22 


12-24 


96-17 


12-66 


96-11 


i3-o8 


9 l 


< 98 


91 


27 


n-94 


97 


22 


12-37 


97- 16 


12.79 


97-10 


l3-22 


98 


99 


98 


.26 


12-07 


98 


21 


12-49 


98-15 


12-92 


98-10 


i3-35 


99 


100 


99 -25 


12-19 


99-20 


12-62 


99-!4 


i3-o5 


99.09 


13-49 


100 


c 

\ a 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


:Lat. 


Dep. 


Lat. 


6 


a 

CO 

s 


8: 


5° 


82 


1° 


82 


i° 


82 


4° 

















































i 
















'* 


102 






TRAVERSE TABLE. 




Table IV. 


a 


8 





8i° 


8i° 


8|° 


\ 

s 

p 1 
















CD 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


p > 


CD 


I 


99 


0-14 


99 


0-14 


0.99 


o-i5 


0.99 


o-i5 


I 


2 


1 


98 


0-28 


1 


98 


0- 


29 


1 • 


98 


0- 


3o 


I- 


98 





3o 


2 


3 


2 


97 


0-42 


2 


97 





43 


2- 


97 





44 


2 


97 





46 


3 


4 


3 


9 6 


o-56 


3 


96 





57 


3- 


96 


0- 


5 9 


3 


9 5 





61 


4 


5 


4 


9 5 


0-70 


4 


9 5 





72 


4- 


9 5 





74 


4 


94 





76 


5 


6 


5 


94 


0-84 


5 


94 





86 


5- 


93 





89 


5 


93 





9! 


6 


7 


6 


9 3 


0-97 


6 


93 


1 


00 


6 


92 


1 


o3 


6 


92 


1 


06 


7 


8 


7 


92 


I'll 


7 


92 


1 


i5 


7 


9 1 


1 


18 


7 


9 1 


1 


22 


8 


9 


8 


9i 


1-25 


8 


9 1 


1 


29 


8 


00 


1 


33 


8 


90 


1 


37 


9 


10 


9 


90 


1-39 


9 


90 


1 


43 


9 


89 


1 


48 


9 


88 


1 


52 


10 


ii 


10 


89 


1-53 


10 


89 


I 


58 


10 


88 


1 


63 


10 


87 


1 


67 


11 


12 


11 


88 


1-67 


11 


88 


I 


72 


11 


87 


1 


77 


11 


86 


1 


83 


12 


i3 


12 


87 


i- 81 


12 


87 


1 


87 


12 


86 


1 


92 


12 


85 


1 


98 


i3 


U 


i3 


86 


1-95 


i3 


86 


2 


01 


i3 


85 


2 


07 


i3 


84 


2 


i3 


14 


i5 


14 


85 


2- 0Q 


14 


85 


2 


i5 


14 


84 


2 


22 


14 


83 


2 


28 


i5 


16 


i5 


84 


2-2J 


i5 


84 


2 


3o 


i5 


82 


2 


36 


i5 


81 


2 


43 


16 


a 


16 


83 


2-37 


16 


83 


2 


44 


16 


81 


2 


5i 


16 


80 


2 


5 9 


12 


n 


82 


2-5l 


17 


81 


2 


58 


17 


80 


2 


66 


17 


79 


2 


74 


19 


18 


82 


2-64 


18 


80 


2 


73 


18 


79 


2 


81 


18 


78 


2 


89 


*9 


20 


19 


81 


2-78 


19 


79 


2 


87 


J 9 


78 


-2 


96 


19 


77 


3 


04 


20 


21 


20 


80 


2-92 


20 


78 


3 


01 


20 


77 


3 


10 


20 


76 


3 


19 


21 


22 


21 


79 


3-o6 


21 


77 


3 


16 


21 


76 


3 


25 


21 


74 


3 


35 


22 


23 


22 


78 


3-20 


22 


76 


3 


3o 


22 


75 


3 


40 


22 


73 


3 


5o 


23 


24 


23 


77 


3.34 


23 


75 


3 


44 


23 


74 


3 


55 


23 


72 


3 


65 


24 


25 


24 


76 


3.48 


24 


74 


3 


5q 


24 


73 


3 


70 


24 


7 1 


3 


80 


25 


26 


25 


75 


3-62 


25 


73 


3 


73 


25 


7i 


3 


84 


25 


70 


3 


96 


26 


27 


26 


74 


3.76 


26 


72 


3 


87 


26 


70 


3 


99 


26 


69 


4 


11 


27 


28 


27 


73 


3-90 


27 


7i 


4 


02 


27 


69 


4 


14 


27 


67 


4 


26 


28 


^ 9 


28 


72 


4-04 


28 


70 


4 


16 


28 


68 


4 


29 


28 


66 


4 


41 


29 


3o 


29 


7i 


4-i8 


29 


69 


4 


3o 


29 


67 


4 


43 


29 


65 


4 


56 


3o 


3i 


3o 


70 


4-3i 


3o 


68 


4 


45 


3o 


66 


4 


58 


3o 


64 


4 


72 


3i 


32 


3i 


69 


4-45 


3i 


67 


4 


5 9 


3i 


65 


4 


73 


3i 


63 


4 


87 


32 


33 


32 


68 


4-5 9 


32 


66 


4 


74 


32 


64 


4 


88 


32 


62 


5 


02 


33 


34 


33 


67 


4-73 


33 


65 


4 


88 


33 


63 


5 


o3 


33 


60 


5 


l l 


34 


35 


34 


66 


4-8 7 


34 


64 


5 


02 


34 


62 


5 


17 


34 


5 9 


5 


32 


35 


36 


35 


65 


5-oi 


35 


63 


5 


17 


35 


60 


5 


32 


35 


58 


5 


48 


36 


U 


36 


64 


5-i5 


36 


62 


5 


3i 


36 


59 


5 


47 


36 


5 7 


5 


63 


37 


37 


63 


5-29 


37 


61 


5 


45 


37 


58 


5 


62 


37 


56 


5 


78 


38 


3 9 


38 


62 


5-43 


38 


60 


5 


60 


38 


5 7 i 5 


76 


38 


55 


5 


9 3 


39 


40 


3 9 


61 


5.57 


39 


5 9 


5 


74 


3 9 


56 5 


9 1 


3 9 


53 


6 


08 


40 


41 


4o 


60 


5-71 


40 


58 


5 


88 


4o 


55 ! 6 


06 


4o 


52 


6 


24 


4i 


; 42 


4i 


5 9 


5-85 


41 


57 


6 


o3 


4i 


54 | 6 


21 


41 


5i 


6 


39 


42 


43 


42 


58 


5.98 


42 


56 


6 


n 


42 


53 1 6 


36 


42 


5o 


6 


54 


43 


44 


43 


57 


6-12 


43 


•54 


6 


3i 


43 


52 6 


5o 


43 


49 


6 


69 


44 


45 


44 


56 


6-26 


44 


53 


6 


46 


44 


5i j 6 


65 


44 


48 


6 


85 


45 


46 


45 


55 


6-4o 


45 


•52 


6 


60 


45 


49 6 


80 


45 


•46 


7 


00 


46 


47 


46 


54 


6-54 


46 


5i 


6 


74 


46 


48 1 6 


93 


46 


45 


7 


i5 


47 


48 


47 


53 


6-68 


47 


5o 


6 


a 


47 


47 ; 7 


•09 


47 


44 


7 


3o 


48 


i 9 


48 


52 


6-82 


48 


•49 


7 


48 


•46 7 


•24 


48 


43 


7 


45 


49 


5o 


49-51 


6.96 


49-48 


7-17 


49-45 


7-3 9 


49-42 
Dep. 


7-61 


5o 





c 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Lat. 


a 

00 

5 


8 


2° 


8I|o 


81i° 


81 


4° 
















„ 



Table IV. 




TRAVERSE TABLE. 






103 


d 
3" 

o 
a 


£ 





H 





8i° 


8, 


P 


g 

a 

a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


5o-5o 


7-10 


5o-47 


7-32 


5o-44 


7-54 


5o-4i 


7.76 


5i 


52 


5i-49 


7-24 


5i-46 


7 


46 


5i-43 


7-69 


5i .39 


7-91 


52 


53 


52-48 


7-38 


52-45 


7 


61 


52-42 


7-83 


52-38 


8-o6 


53 


54 


53.47 


7-52 


53-44 


7 


75 


53-4i 


7.98 


53.37 


8-21 


54 


55 


54-46 


7-65 


54-43 


7 


89 


54-4o 


8-i3 


54-36 


8.37 


55 


56 


55-46 


7.79 


55-42 


8 


04 


55-38 


8-28 


55-35 


8-52 


56 


57 


56-45 


7- 9 3 


56-4i 


8 


18 


56-37 


8-43 


56-34 


8-67 


5 7 


58 


5 7 -44 


8-07 


57-40 


8 


32 


57-36 


8-5 7 


57-32 


8-82 


58 


5 9 


58-43 


8-21 


58-3o 


8 


47 


58-35 


8-72 


58- 3i 


8.98 


5 9 


6o 


59-42 


8-35 


5 9 -38 


8 


61 


5 9 -34 


8-87 


59.30 


9>i3 


60 


6i 


6o-4i 


8.49 


60-37 


8 


75 


60 -33 


9-02 


60-29 


9.28 


61 


62 


61 -4o 


8-63 


61 -36 


8 


90 


6i-32 


9-16 


61-28 


9-43 


62 


63 


62-39 


8-77 


62-35 


9 


04 


62-3i 


9-3i 


62-27 


9-58 


63 


64 


63-38 


8.91 


63-34 


9 


18 


63-3o 


9.46 


63-26 


9-74 


64 


65 


64-37 


9-o5 


64-33 


9 


33 


64-29 


9-61 


64-24 


9.89 


65 


66 


65-36 


9-19 


65-32 


9 


47 


65-28 


9-76 


65-23 


io-o4 


66 


67 


66-35 


9-32 


66-3i 


9 


61 


66-26 


9.90 


66-22 


10-19 


67 


68 


67-34 


9.46 


67-30 


9 


76 


67-25 


io-o5 


67-21 


io-34 


68 


69 


68-33 


9-60 


68- 29 


9 


90 


68-24 


10-20 


68-20 


io-5o 


69 


70 


69-32 


9-74 


69-28 


10 


04 


69-23 


io-35 


69-19 


10-65 


70 


7i 


70 -3i 


9-88 


70-27 


10 


19 


70-22 


10.49 


70-17 


io-8o 


7i 


72 


7i-3o 


10-02 


71-25 


10 


33 


71-21. 


10-64 


71 -i6 


10-95 


72 


73 


72-29 


10-16 


72-24 


10 


47 


72-20 


10-79 


72-i5 


II-IO 


73 


H 


73-28 


io-3o 


73-23 


10 


62 


73-19 


10-94 


73-U 


11-26 


74 


75 


74-27 


10-44 


74-22 


10 


76 


74-i8 


11-09 


74- 13 


11.41 


75 


76 


75-26 


io-58 


75-21 


10 


9 1 


75.17 


II -23 


75-12 


II-56 


76 


% 


76-25 


10-72 


76-20 


11 


o5 


76-i5 


n-38 


76-10 


11. 71 


77 


77-24 


io-86 


77.19 


11 


*9 


77'U 


n-53 


77 -oo 


11-87 


78 


29 


78-23 


10-99 


78-18 


11 


34 


78-i3 


n-68 


78-08 


12-02 


79 


80 


79-22 


11. i3 


79-17 


11 


48 


79-12 


11-82 


79-07 


12-17 


80 


81 


80-21 


11-27 


80-16 


11 


62 


8o- 1 1 


11.97 


80-06 


12-32 


81 


82 


8l -20 


ii-4i 


8i-i5 


11 


77 


8i- 10 


12-12 


8i-o5 


12-47 


82 


83 


82-19 


n-55 


82-14 


11 


9 1 


82-09 


12-27 


82-o3 


12-63 


83 


84 


83- 18 


11-69 


83-i3 


12 


o5 


83- 08 


12-42 


83-02 


12-78 


84 


85 


84-17 


n-83 


84-12 


12 


20 


84-07 


12-56 


84-01 


12-93 


85 


86 


85- 16 


11.97 


85-u 


12 


34 


85- 06 


12-71 


85-oo 


i3-o8 


86 


87 


86-i5 


12-11 


86-10 


12 


48 


86-04 


12-86 


85.99 


13-23 


87 


88 


87-14 


12-25 


87-09 


12 


63 


87-03 


i3-oi 


86-98 


i3-3o 


88 


89 


88-i3 


12-39 


88- 08 


12 


77 


88-02 


i3-i6 


87.96 


i3.54 


89 


90 


89-12 


12-53 


89-07 


12 


9 1 


89-01 


i3-3o 


88- 9 5 


13.69 


90 


9i 


90-11 


12-66 


90-06 


i3 


06 


90-00 


i3-45 


89-94 


i3-84 


9i 


92 


91-10 


12.80 


91 -o5 


i3 


20 


90-90 


i3-6o 


90-93 


i4-oo 


92 


9 3 


92-09 


12-94 


92-04 


i3 


34 


91-98 


13-75 


91-92 


i4-i5 


93 


9| 


93.09 


i3-o8 


93 -o3 


i3 


49 


92-97 


i3-8 9 


92-91 


i4-3o 


94 


9 5 


94-08 


l3-22 


94-02 


i3 


63 


93-96 


14-04 


9 3-8o 


14-45 


9 5 


96 


95-07 


13-36 


95-01 


i3 


78 


94-96 


14-19 


9 4-88 


14-60 


96 


97 


96-06 


i3-5o 


96-00 


i3 


92 


93-93 


14-34 


95-87 


14-76 


97 


98 


97 -o5 


i3-64 


96-99 


14 


06 


96-92 


14-49 


96-86 


14-91 


98 


99 


98-04 


13-78 


97-98 


14 


21 


97-91 


14-63 


97-85 


i5-o6 


99 


100 


99 -o3 


13-92 


98-97 


14-35 


98-90 


14-78 


98-84 


I5-2I 


100 


J 

Distance. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


a 

a 

IB 

Q 


85 


1° 


81 


1° 




81 


1° 


81 


1° 



104: 






TRAVERSE TABLE. 




Table IV. 


b 

55' 


9 


3 


9i° 


9i° 


9£° 


O 

go' 

p 

3 
O 
CD 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


0-99 


0-16 


0.99 


0-16 


0.99 


0-17 


0.99 


0-17 


I 


2 


1.98 


o-3i 


I- 


97 


0- 


32 


1-97 


0-33 


I- 


97 


0-34 


2 


3 


2-96 


o-47 


2- 


96 


0- 


48 


2-96 


o-5o 


2 


96 


o-5i 


3 


4 


3- 9 5 


o-63 


3- 


9 5 


0- 


64 


3- 9 5 


o-66 


3 


94 


o-68 


4 


5 


4-94 


0.78 


4- 


9 3 


0- 


80 


4- 9 3 


o-83 


4 


93 


o-85 


5 


6 


5- 9 3 


0-94 


5- 


92 


0- 


96 


5-92 


0-99 


5 


9 1 


1-02 


6 


2 


6-91 


1 -10 


6 


9 1 


1 


i3 


6-oo 


1-16 


6 


90 


1-19 


I 


7. OO 


1-25 


7 


90 


i- 


29 


7-89 


1-32 


7 


88 


i-35 


9 


8-S 9 


1 -4i 


8 


88 


1 


45 


8-88 


1-49 


8 


87 


1-52 


9 


10 


9.88 


i-56 


9 


87 


1 


61 


9-86 


1-65 


9 


86 


1-69 


10 


II 


10.86 


1-72 


10 


86 


1 


77 


10-85 


1.82 


10 


84 


i-86 


11 


12 


n-85 


1.88 


11 


84 


1 


93 


11-84 


1-98 


11 


83 


2-o3 


12 


i3 


12-84 


2-o3 


12 


83 


2 


09 


12-82 


2-l5 


12 


81 


2-20 


i3 


14 


i3-83 


2-19 


i3 


82 


2 


25 


i3-8i 


2-3l 


i3 


80 


2-37 


14 


i5 


14-82 


2.35 


14 


80 


2 


4i 


U-79 


2.48 


14 


78 


2-54 


i5 


16 


i5-8o 


2-5o 


i5 


79 


2 


5 7 


15-78 


2-64 


i5 


77 


2-71 


16 


n 


16.79 


2-66 


16 


78 


2 


73 


16-77 


2-8l 


16 


75 


2-88 


17 


18 


17.78 
18-77 


2-82 


17 


77 


2 


89 


17-7.5 


2-97 


17 


74 


3-o5 


18 


19 


2-97 


18 


7 5 


3 


o5 


18-74 


3-i4 


18 


73 


3-22 


19 


20 


19.75 


3-i3 


19 


74 


3 


21 


19.73 


3-3o 


19 


7i 


3.39 


20 


21 


20-74 


3-29 


20 


73 


3 


38 


20-71 


3-47 


20 


70 


3-56 


21 


22 


21-73 


3-44 


21 


7i 


3 


54 


21 -70 


3-63 


21 


.68 


3.73 


22 


23 


22-72 


3-6o 


22 


70 


3 


70 


22-68 


3-8o 


22 


67 


3-90 


23 


24 


23-70 


3.75 


23 


69 


3 


86 


23-67 


3.96 


23 


• 65 


4-o6 


24 


25 


24-69 


3.91 


24 


67 


4 


02 


24-66 


4-i3 


24 


• 64 


4-23 


25 


26 


25-68 


4-07 


25 


66 


4 


18 


25-64 


4-29 


25 


.62 


4.40 


26 


27 


26-67 


4-22 


26 


65 


4 


■34 


26-63 


4-46 


26 


61 


4-57 


27 


28 


27-66 


4-38 


27 


64 


4 


5o 


27-62 


4-62 


27 


.60 


4-74 


28 


2 9 


28-64 


4-54 


28 


62 


4 


66 


28-60 


4-79 


28 


58 


4-91 


29 


3o 


29-63 


4.69 


29 


61 


4 


82 


29.59 


4-95 


29 


5 7 


5- 08 


3o 


3i 


3o-62 


4-85 


3o 


60 


4 


98 


3o-57 


5-12 


3o 


55 


5-25 


3i 


32 


3i-6i 


5-oi 


3i 


58 


5 


14 


3i-56 


5-28 


3i 


54 


5-42 


32 


33 


32-59 


5-i6 


32 


57 


5 


3o 


32-55 


5-45 


32 


52 


5-5 9 


33 


34 


33-58 


5-32 


33 


56 


5 


■47 


33-53 


5-6i 


33 


5i 


5- 7 6 


34 


35 


34-5 7 


5-48 


34 


■54 


5 


63 


34-52 


5.78 


34 


49 


5- 9 3 


35 


36 


35-56 


5-63 


35 


• 53 


5 


■79 


35-5i 


5-94 


35 


• 48 


6-io 


36 


37 


36-54 


5.79 


36 


• 02 


5 


9 5 


36-49 


6- 11 


36 


•47 


6-27 


37 


38 


37.53 


5-94 


37 


•5i 


6 


•11 


37.48 


6-27 


37 


•45 


6-44 


38 


3 9 


38-52 


6-io 


38 


.40 


6 


•27 


38-47 


6-44 


38 


•44 


6-6o 


39 


40 


39-5i 


6-26 


3 9 


.48 


6 


■43 


39-45 


6-6o 


39 


•42 


6-77 


4o 


4i 


4o -5o 


6-41 


4o 


•47 


6 


• 5o 


40-44 


6-77 


4o 


•4i 


6-94 


41 


42 


4i-48 


6-5 7 


4i 


■45 


6 


.75 


4i-42 


6-92 


4i 


• 3 9 


7-11 


42 


43 


42-47 


6- 7 3 


42 


•44 


6 


.91 


42-4i 


7.10 


42 


• 38 


7-28 


43 


44 


43-46 


6-88 


43 


• 43 


7 


• 07 


43-4o 


7-26 


43 


• 36 


7-45 


44 


45 


44-45 


7-o4 


44 


•4i 


7 


-23 


44-38 


7-43 


44 


• 35 


7-62 


45 


46 


45-43 


7-20 


45 


• 40 


7 


.39 


45- 3 7 


7.59 


45 


■ 34 


7.79 


46 


47 


46-42 


7-35 


46 


■39 


7 


.55 


46-36 


7.76 


46 


32 


7.96 


47 


48 


47-4i 


7-5i 


47 


• 38 


7 


•72 


47-34 


7-92 


47 


3i 


8-i3 


48 


49 


48-40 


7.67 


48 


-36 


7 


-88 


48-33 


8-09 


48 


29 


8-3o 


4 9 


5o 


49-38 


7-82 


49-35 


8-04 


49.32 


8-25 


49-28 


8-47 


5o 


6 



a 

R3 


Dep. 


Lat. 


Dep. 


Lat. 
\ 


Dep. 


Lat. 


Dep. 


Lat. 


a 

a 














5 


8 


1° 


80f° 


80i° 


80 


1° 


Q 



Table IV. 




TEA VERSE TABLE. 






105 


e 

So 

p 

3 

CD 


9 





n 





9i° 


9|° 


d 

n 
P 


Lat. 


Dep. 


Lat. 


Dep. 


1 
Lat. 


Dep. 


Lat. 


Dep. 


5i 


5o»37 


It 


5o-34 


8-20 


5o-3o 


8-42 


5o-26 


8-64 


5i 


52 


5i-36 


5i -32 


8 


36 


5i- 


29 


8 


58 


5i- 


25 


8-8i 


52 


53 


52-35 


8-29 


52-3i 


8 


52 


52- 


27 


8 


75 


52 


23 


8-98 


53 


54 


53-34 


8-45 


53- 3o 


8 


68 


53 


26 


8 


9 1 


53 


22 


9-14 


54 


55 


54-32 


8-6o 


54-28 


8 


84 


54 


25 


9 


08 


54 


21 


9-3i 


55 


56 


55- 3i 


8-76 


55-27 


9 


00 


55 


23 


9 


24 


55 


IO 


9-48 


56 


5 1 


56 -3o 


8-92 


56-26 


9 


16 


56 


22 


9 


4i 


56 


IO 


9-65 


5 7 


58 


57-29 


9-07 


57-25 


9 


32 


5 7 


20 


9 


57 


57 


16 


9-82 


58 


5 9 


58-27 


9-23 


58-23 


9 


48 


58 


19 


9 


74 


58 


i5 


9.99 


5 9 


6o 


59-26 


9.39 


59-22 


9 


64 


5 9 


l8 


9 


90 


5 9 


i3 


10-16 


60 


6i 


6o-25 


9.54 


60'2I 


9 


81 


60 


16 


10 


07 


60 


12 


10-33 


61 


62 


61-24 


9-70 


61.19 


9 


97 


61 


i5 


10 


23 


61 


10 


io-5o 


62 


63 


62-22 


9.86 


62-18 


10 


i3 


62 


14 


10 


40 


62 


09 


10-67 


63 


64 


63-21 


IO-OI 


63-n 


10 


45 


63 


12 


10 


56 


63 


08 


10-84 


64 


65 


64-20' 


10-17 


64-i5 


10 


64 


11 


10 


73 


64 


06 


II-OI 


65 


66 


65-19 


10-32 


65-i4 


10 


61 


65 


09 


10 


89 


65 


o5 


11. 18 


66 


67 


66-18 


10-48 


66-i3 


10 


77 


66 


08 


11 


06 


66 


o3 


n-35 


67 


68 


67-16 


10-64 


67-12 


10 


93 


67 


07 


11 


22 


67 


02 


11-52 


68 


69 


68-i5 


10-79 


68-io 


11 


09 


68 


o5 


11 


3 9 


68 


00 


11-69 


69 


70 


69-14 


10-93 


69-09 


11 


2D 


69 


04 


11 


55 


68 


99 


n-85 


70 


71 


70-i3 


nil 


70-08 


11 


41 


70 


o3 


n 


72 


69 


97 


12-02 


7i 


72 


71-11 


11-26 


71-06 


11 


5 7 


7i 


01 


11 


88 


70 


96 


12-19 


72 


73 


72-10 


11.42 


72-o5 


11 


73 


72 


00 


12 


o5 


7i 


9 5 


12-36 


73 


7 f 


73-09 


ii-58 


73-o4 


11 


89 


72 


99 


12 


21 


72 


93 


12-53 


74 


7 5 


74-08 


ii- 7 3 


74-02 


12 


06 


73 


97 


12 


38 


73 


92 


12-70 


75 


76 


75-o6 


11-89 


75-oi 


12 


22 


74 


96 


12 


54 


74 


90 


I2-8T 


76 


? 


76-o5 


I2-0D 


76-00 


12 


38 


75 


94 


12 


7i 


75 


89 


i3-o4 


7 2 


77-04 


12-20 


76-99 


12 


54 


76 


93 


12 


87 


76 


87 


13-21 


78 


11 


78-o3 


12-36 


77-97 


12 


70 


77 


92 


i3 


04 


77 


86 


13-38 


2 Q 


79-02 


I2-5l 


78-96 


12 


86 


78 


90 


i3 


20 


78 


84 


i3-55 


80 


81 


80 -00 


12-67 


79.95 


i3 


02 


79 


8 9 


i3 


37 


79 


83 


i3-72 


81 


82 


80 -99 


12-83 


8o- 9 3 


i3 


18 


80 


88 


i3 


53 


80 


82 


i3-8 9 


82 


83 


81-98 


12-98 


81-92 


i3 


34 


81 


86 


i3 


70 


81 


-8o 


14-06 


83 


84 


82-97 


i3-i4 


82-91 


i3 


5o 


82 


85 


i3 


86 


82 


79 


14-23 


84 


85 


83-95 


i3-3o 


83-8 9 


i3 


66 


83 


83 


14 


o3 


83 


'77 


U-3 9 


85 


86 


84-94 


13-45 


84-88 


i3 


82 


84 


82 


14 


•19 


84 


.76 


14-56 


86 


& 


85 . 9 3 


i3-6i 


85-87 


i3 


98 


85 


81 


14 


■36 


85 


■74 


14-73 


ll 


86-92 


13.77 


86-86 


14 


i5 


86 


■79 


14 


52 


86 


- 7 3 


14-90 


89 


87-90 


i3-92 


87-84 


14 


3i 


87 


.78 


14 


•69 


87 


•7i 


1 5-07 


89 


90 


88-89 


14-08 


88-83 


14 


47 


88 


■77 


14 


•85 


88 


.70 


i5-24' 


90 


91 


89-88 


14-24 


89-82 


14 


• 63 


89 


•75 


i5 


■ 02 


89 


.69 


i5-4i 


9i 


92 


90-87 


i4-3o 


90-80 


14 


'79 


90 


74 


i5 


• 18 


90 


.67 


15-58 


9? 


9 3 


91-86 


14-55 


91-79 


14 


• 9 5 


9i 


72 


i5 


• 35 


9 1 


■ 66 


15-75 


9 3 


9f 


92-84 


14-70 


92-78 


i5 


-11 


92 


7i 


i5 


5i 


92 


• 64 


15.92 


94 


9 5 


9 3-83 


U-86 


93-76 


i5 


■27 


93 


70 


i5 


68 


93 


• 63 


16-09 


9 5 


96 


94-82 


l5-02 


94-75 


i5 


•43 


9 4 


68 


i5 


84 


94 


61 


16-26 


96 


91 


95-8i 


15.17 


9 5-74 


i5 


-5 9 


9 5 


67 


16 


01 


9 5 


• 60 


i6-43 


97 


98 


96-79 


15-33 


96-73 


i5 


•75 


96 


66 


16 


n 


96 


58 


16-60 


98 


99 


97-78 


i5-49 


97-71 


i5 


• 91 


97 


64 


16 


34 


97 


■57 


16-77 


99 


100 


98.77 


15-64 


98-70 


16-07 


98- 63 


i6-5o 


98- 56 


l6 '9 3 . 


100 


a> 


a 
a 

in 

5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


co 



a 

d 

Q 


8 


L° 


80 


1° 


80 


i° 


80 


\° 



5* 



106 






TRAVERSE TABLE. 




Table IV. 


o 

& 

3 
o 
p 


10° 


10i° 


10 


*° 


10 


1° 


9 
00' 

s 

CD 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


0- 9 8 


0-17 


0-98 


0-18 


0-98 


0-l8 


0.98 


0-19 


I 


2 


I 


97 





35 


I 


97 


o-36 


I 


97 


o-36 


1-96 


O.37 


2 


3 


2 


9 5 





52 


2 


9 5 


0-53 


2 


9 5 


o-55 


2-95 


o-56 


3 


4 


3 


9 4 





S* 


3 


94 


0-71 


3 


9 3 


0-73 


3. 9 3 


0-75 


4 


5 


4 


92 





87 


4 


92 


0-89 


4 


92 


0-91 


4-gi 


0-93 


5 


6 


5 


91 


1 


04 


5 


s° 


1 -07 


5 


90 


1-09 


5.89 


I-I2 


6 


7 


6 


89 


1 


22 


6 


89 


1-25 


6 


88 


1-28 


6-88 


i-3i 


' I 





7 


88 


1 


3 9 


7 


87 


1-42 


7 


87 


1-46 


7-86 


1-49 


9 


8 


86 


1 


56 


8 


86 


I' 60 


8 


85 


1-64 


8-84 


1.68 


9 


10 


9 


85 


1 


74 


9 


84 


1-78 


9 


83 


1-82 


9.82 


1.87 


10 


ii 


10 


83 


1 


9 1 


10 


82 


1-96 


10 


82 


2 -00 


10. 81 


2>o5 


11 


12 


11 


82 


2 


08 


11 


81 


2-14 


11 


80 


2-19 


11.79 


2-24 


12 


i3 


12 


80 


2 


26 


12 


79 


2-3l 


12 


78 


2-37 


12-77 


2-42 


i3 


i4 


i3 


79 


2 


43 


i3 


78 


2-49 


i3 


]l 


2-55 


13.75 


2-6l 


14 


i5 


14 


77 


2 


60 


14 


76 


2-67 


14 


2-73 


14-74 


2-80 


i5 


16 


i5 


76 


2 


78 


i5 


74 


2-85 


i5 


73 


2-92 


15.72 


2.98 


16 


17 


16 


74 


2 


9 5 


16 


73 


3-o3 


16 


72 


3-io 


16-70 


3.17 


n 


18 


17 


73 


3 


i3 


17 


7 1 


3-20 


17 


70 


3-28 


17.68 


3-36 


18 


19 


18 


71 


3 


3o 


18 


70 


3-38 


18 


68 


3-46 


18-67 


3-54 


19 


20 


19 


70 


3 


47 


19 


68 


3-56 


19 


67 


3-64 


I9>65 


3.73 


20 


21 


20 


68 


3 


65 


20 


66 


3-74 


20 


65 


3-83 


20-63 


3.92 


21 


22 


21 


67 


3 


82 


21 


65 


3-91 


21 


63 


4-oi 


2I-6l 


4-io 


22 


23 


22 


65 


3 


99 


22 


63 


4-09 


22 


61 


4-19 


22-60 


4-29 


23 


24 


23 


64 


4 


l l 


23 


62 


4-27 


23 


60 


4-3 7 


23-58 


4-48 


24 


25 


24 


62 


4 


34 


24 


60 


4-45 


24 


58 


4-56 


24-56 


4-66 


25 


26 


25 


61 


4 


5i 


25 


5 9 


4-63 


25 


56 


4-74 


25-54 


4-85 


26 


27 


26 


5 9 


4 


69 


26 


57 


4-8o 


26 


55 


4-92 


26-53 


5-o4 


27 


28 


27 


5 7 


4 


86 


27 


55 


4-98 


27 


53 


5-io 


27-5i 


5-22 


28 


29 


28 


56 


5 


04 


28 


54 


5-i6 


28 


5i 


5-28 


28-49 


5.41 


29 


3o 


29 


54 


5 


21 


29 


52 


5-34 


29 


5o 


5-47 


29-47 


5-6o 


3o 


3i 


3o 


53 


5 


38 


3o 


5i 


5-52 


3o 


48 


5-65 


3o-46 


5.78 


3i 


32 


3i 


5i 


5 


56 


3i 


49 


5-69 


3i 


46 


5-83 


3i-44 


5.97 


32 


33 


32 


5o 


5 


73 


32 


47 


5.87 


32 


45 


6-oi 


32-42 


6-i6 


33 


34 


33 


48 


5 


90 


33 


46 


6-o5 


33 


43 


6-20 


33-4o 


6-34 


34 


35 


34 


47 


6 


08 


34 


44 


6-23 


34 


4i 


6-38 


34-39 


6-53 


35 


36 


35 


45 


6 


25 


35 


43 


6-41 


35 


40 


6-56 


35.37 


6-71 


36 


37 


36 


44 


6 


42 


36 


41 


6-58 


36 


38 


6-74 


36-35 


6-90 


37 


38 


37 


£ 2 


6 


60 


37 


3 9 


6-76 


37 


36 


6-92 


37.33 


7.09 


38 


3 9 


38 


4*i 


6 


77 


38 


38 


6-94 


38 


35 


7. 11 


38-32 


7-27 


39 


4o 


3 9 


3 9 


6 


9 5 


39 


36 


7-12 


3 9 


33 


7.29 


39-3o 


7-46 


40 


41 


4o 


38 


7 


12 


4o 


35 


7-3o 


4o 


3i 


7-47 


40-28 


7-65 


4i 


42 


4i 


36 


7 


29 


4i 


33 


7'47 


4i 


3o 


7-65 


41-26 


7-83 


42 


43 


42 


35 


7 


47 


42 


3i 


7-65 


42 


28 


7-84 


42-25 


8-02 


43 


44 


43 


33 


7 


64 


43 


3o 


7-83 


43 


26 


8-02 


43-23 


8-21 


44 


45 


44 


32 


7 


81 


44 


28 


8-oi 


44 


25 


8-20 


44-21 


8-3 9 


45 


46 


45 


3o 


7 


99 


45 


27 


8-19 


45 


23 


8-38 


45-iq 


8-58 


46 


47 


46 


29 


8 


16 


46 


25 


8-36 


46 


21 


8-57 


46-18 


8-77 


47 


48 


47 


27 


8 


34 


47 


23 


8-54 


47 


20 


8- 7 5 


47- 16 


8- 9 5 


48 


$ 


48 


26 


8 


5i 


48 


22 


8-72 


48 


18 


8- 9 3 


48-14 


9-14 


49 


5o 


49-24 


8-68 


49-20 


8-90 


49-16 


9-n 


•49-12 


9-33 


5o 





Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


G3 


Distan 


















CO 

Q 


8 


3° 


79 


1° 


79 


h° 


79 


k° 



Table IV. 




TRAVERSE TABLE. 




107 


g 

p 

3 

9 


10° 


1(H° 


10£° 


10 


1° 


g 

3 

CD 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


5o-23 


8-86 


. 5o-l9 


9-08 


5o-i5 


9.29 


5o-io 


9«5i 


Si 


52 


5l-2I 


9-o3 


5i -17 


9-25 


5i 


i3 


9.48 


5i 


09 


9 


70 


52 


53 


52-19 


9-20 


52-i5 


9-43 


52 


11 


9.66 


52 


07 


9 


89 


53 


54 


53-18 


9-38 


53-i4 


9-61 


53 


10 


9.84 


53 


o5 


10 


07 


54 


55 


54-i6 


9-55 


54-12 


9-79 


54 


08 


10-02 


54 


o3 


10 


26 


55 


56 


55- 15 


9.72 


55-ii 


9-96 


55 


06 


10-21 


55 


02 


10 


45 


56 


5i 


56-i3 


9-90 


56-09 


io-i4 


56 


o5 


10-39 


56 


00 


10 


63 


u 


58 


57-12 


10-07 


57-07 


10-32 


57 


o3 


10-57 


56 


98 


10 


82 


5 9 


58-10 


10-25 


58. 06 


io- 5o 


58 


01 


IO.75 


5 7 


96 


11 


00 


59 


6o 


59-09 


10-42 


59-04 


io-68 


5 9 


00 


IO.93 


58 


9 5 


11 


J 9 


60 


6i 


60-07 


10-59 


60 -o3 


10-85 


5 9 


98 


11-12 


5 9 


93 


11 


38 


61 


62 


61 -06 


10.77 


6i-oi 


11 -o3 


60 


96 


11 -3o 


60 


9 1 


11 


56 


62 


63 


62-04 


10-94 


61-99 


11-21 


61 


9 5 


n-48 


61 


89 


11 


75 


63 


64 


63 -o3 


1 1 ♦ 1 1 


62.98 


11-39 


62 


93 


n-66 


62 


88 


11 


94 


64 


65 


64-01 


11-29 


63 -96 


11-57 


63 


9 1 


n-85 


63 


86 


12 


12 


65 


66 


65-oo 


11-46 


64-95 


-U-74 


64 


89 


12 -o3 


64 


84 


12 


3i 


66 


67 


65- 98 


u-63 


65- 9 3 


11 -92 


65 


88 


12-21 


65 


82 


12 


5o 


67 


68 


66-97 


11. 81 


66-91 


12- 10 


66 


86 


12.39 


66 


81 


12 


68 


68 


69 


67.95 


11-98 


67-90 


12-28 


67 


84 


12-57 


67 


79 


12 


87' 


69 


70 


68-94 


I2-l6 


68-88 


12-46 


68 


83 


12-76 


68 


77 


i3 


06 


70 


7i 


69-92 


12-33 


69.87 


12-63 


69 


81 


12-94 


69 


7 5 


i3 


24 


7i 


72 


70-91 


12 -5o 


70-85 


12.81 


70 


79 


l3-I2 


70 


74 


i3 


43 


72 


73 


71-89 


12.68 


71-83 


I2-Q9 


7i 


78 


i3-3o 


7i 


72 


i3 


62 


73 


74 


72-88 


12-85 


72-82 


I3-I7 


72 


76 


i3-49 


72 


70 


i3 


80 


74 


7 5 


73-86 


l3-02 


73-8o 


i3-35 


73 


74 


13-67 


73 


68 


i3 


99 


75 


76 


74-85 


l3-20 


74-79 


i3-52 


74 


73 


i3-85 


74 


67 


14 


18 


76 


77 


75-83 


13.37 


75.77 


i3-70 


75 


7i 


i4-o3 


75 


65 


14 


36 


77 


78 


76-82 


13.54 


76-76 


i3-88 


76 


69 


14-21 


76 


63 


14 


55 


78 


79 


77-80 


13.72 


77-74 


14-06 


77 


68 


14-40 


77 


61 


14 


74 


I 9 


80 


78-78 


13.89 


78-72 


14-24 


78 


66 


14-58 


78 


60 


14 


92 


80 


81 


79-77 


14-07 


79.71 


U-4i 


79 


64 


14-76 


79 


58 


i5 


11 


81 


82 


80-75 


14-24 


80-69 


14-59 


80 


63 


14-94 


80 


56 


i5 


29 


82 


83 


81 -74 


14-41 


81-68 


J 4-77 


81 


61 


i5-i3 


81 


54 


i5 


48 


83 


84 


82-72 


14-59 


82-66 


14-95 


82 


5 9 


i5-3i 


82 


53 


i5 


67 


84 


85 


83.71 


14-76 


83-64 


i5-i3 


83 


58 


i5-49 


83 


5i 


i5 


85 


85 


86 


84-69 


14-93 


84-63 


i5-3o 


84 


56 


15-67 


84 


49 


16 


04 


86 


87 


85-68 


i5-ii 


85- 61 


15-48 


85 


54 


i5-85 


85 


47 


16 


23 


87 


88 


86-66 


i5-28 


86-6o 


15-66 


86 


53 


16-04 


86 


46 


16 


4i 


88 


89 


87 -65 


i5-45 


8 7 -58 


i5-84 


87 


5i 


16-22 


87 


44 


16 


60 


89 


90 


88-63 


i5-63 


83-56 


i6-oi 


88 


4 9 


i6-4o 


88 


42 


16 


79 


90 


9 1 


89-62 


i5-8o 


89.55 


16-19 


89 


48 


16. 58 


89 


4o 


16 


97 


9i 


92 


90-60 


15.98 


90-53 


i6-3 7 


90 


46 


16-77 


90 


3.9 


n 


16 


9 2 


93 


91-59 


i6-i5 


91-52 


i6.55 


9 1 


44 


i6- 9 5 


91 


37 


H 


35 


93 


94 


92 -5 7 


i6-32 


92 -5o 


i6- 7 3 


92 


43 


i 7 -i3 


92 


35 


17 


53 


9 i 


9 5 


9 3 -56 


16. 5o 


93-48 


16-90 


93 


4i 


i 7 .3i 


93 


33 


17 


72 


9 l 


9 6 


94-54 


16.67 


94-47 


17-08 


9 4 


3 9 


17-49 


94 


32 


n 


9 1 


96 


97 


9 5-53 


16.84 


95-45 


17-26 


9 5 


38 


17-68 


9^ 


3o 


18 


09 


9 l 


98 


96.51 


17-02 


96-44 


17-44 


96 


36 


17-86 


96 


28 


18 


28 


98 


99 


97 -5o 


17-19 


97-42 


17-62 


97 


34 


18-04 


97 


26 


18 


47 


99 


100 


98-48 


17-36 


98-40 


17.79 


98.33 


18-22 


9 8-25 


i8-65 


100 


a 

5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 

a 

en 

s 


80° 


79|° 


79£° 


79 


1° 





108 






TRAVERSE TABLE. 




Table IV. 




o 

5" 
f 

a 

(5 
P 


11 





lli° 


lli° 


11 


1° 


9 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




I 


0-98 


0-19 


0-98 


0-20 


0-98 


0-20 


0-98 


0-20 


I 




2 


1-96 


o-38 


1-96 


0-39 


1-96 


o-4o 


1-96 


o>4i 


2 




3 


2-94 


0.57 


2-94 


o-5o 


2-94 


o-6o 


2-94 


o-6i 


3 




4 


3- 9 3 


0-76 


3-92 


0-78 


3-92 


o-8o 


3-92 


0-82 


4 




5 


4-91 


0-95 


4.90 


0-98 


4.90 


I -00 


4.90 


1-02 


5 




6 


5-89 


i-i4 


5-88 


I- 17 


5-88 


I«20 


5-87 


1-22 


6 




7 


6-87 


i-34 


6-87 


i.3 7 


6-86 


I .40 


6-85 


1-43 


7 




8 


7-85 


1-53 


7-85 


i-56 


7-84 


I .59 


7-83 


1-63 


8 




9 


8-83 


1.72 


8-83 


1-76 


8-82 


I.79 


8-8i 


1-83 


9 




10 


9-82 


1-91 


9-81 


1-95 


9-80 


1-99 


9-79 


2- 04 


10 




ii 


io-8o 


2«I0 


10.79 


2-l5 


10.78 


2-19 


10.77 


2-24 


11 




12 


11.78 


2-20 


n-77 


2-34 


11-76 


2-39 


11 -75 


2-44 


12 




i3 


12-76 


2.48 


12-75 


2-54 


12-74 


2-59 


12-73 


2-65 


i3 




14 


i3- 7 4 


2-67 


13.73 


2.73 


13.72 


2-79 


13.71 


2-85 


14 




i5 


14-72 


2-86 


14-71 


2-93 


14-70 


2-99 


14-69 


3- 06 


i5 




16 


i5- 7 i 


3-o5 


15-69 


3-12 


15-68 


3- 19 


15-66 


3-26 


16 




S 


16-69 


3-24 


16-67 


3-32 


16.66 


3-3 9 


16-64 


3-46 


17 




17.67 


3-43 


17-65 


3-5i 


17-64 


3-5 9 


17-62 


3-66 


18 




x 9 


i8-65 


3-63 


18. 63 


3.71 


18-62 


3-79 


18-60 


3-87 


19 




20 


i 9 -63 


3-82 


19-62 


3.90 


19-60 


3-99 


19-58 


4-07 


20 




21 


20-6l 


4-oi 


20- 60 


4> 10 


20-58 


4-19 


20-56 


4-28 


21 




22 


21 -6o 


4-20 


21-58 


4-29 


21-56 


4-3 9 


21-54 


4-48 


M 




23 


22-58 


4-3 9 


22-56 


4-49 


22-54 


4-5 9 


22-52 


4-68 


23 




24 


23-56 


4-58 


23-54 


4-68 


23-52 


4-78 


23 -5o 


4.89 


24 




25 


24-54 


4-77 


24-52 


4-88 


24 -5o 


4- 9 8 


24-48 


5.09 


25 




26 


25-52 


4.96 


2D-D0 


5-07 


25-48 


5-i8 


25-46 


5-3o 


26 




27 


26-5o 


5-i5 


26-48 


5-27 


26-46 


5-38 


26-43 


5-5o 


27 




28 


27.49 


5-34 


27-46 


5-46 


27-44 


5-58 


27-41 


5-70 


28 




^9 


28-47 


5-53 


28-44 


5-66 


28-42 


5- 7 8 


28-39 


5-QI 


29 




3o 


29.45 


5.72 


29-42 


5-85 


29-40 


5- 9 8 


29.37 


6-n 


3o 




3i 


3o-43 


5-02 


3o-4o 


6-o5 


3o-38 


6-i8 


3o-35 


6-3i 


3i 




32 


3i-4i 


6- 11 


3i -39 


6-24 


3i-36 


6-38 


3i-33 


6-52 


32 




33 


32-39 


6-3o 


32-37 


6-44 


32-34 


6-58 


32-3i 


6-72 


33 




34 


33-38 


6.49 


33-35 


6-63 


33-32 


6-78 


33.29 


6-Q2 


34 




35 


34-36 


6-68 


34-33 


6-83 


34 -3o 


6-98 


34-27 


7-i3 


35 




36 


35-34 


6-87 


35-3i 


7-02 


35-28 


7-l8 


35-25 


7-33 


36 




37 


36-32 


7.06 


36-29 


7. 22 


36-26 


7-38 


36-22 


7.53 


37 




38 


37-3o 


7. 25 


37-27 


7-4i 


37-24 


7-58 


37-20 


7-74 


38 




3q 


38-28 


7-44 


38-25 


7. 61 


38-22 


7.78 


38-i8 


7-94 


39 




4o 


39.27 


7-63 


39-23 


7.80 


39-20 


7-97 


39.16 


8-i5 


4o 




4i 


4o-25 


7.82 


40-21 


8-oo 


4o- 18 


8-17 


4o-i4 


8-35 


4i 




42 


4i-23 


8-oi 


41.19 


8-19 


4i-i6 


8-3 7 


4I-I2 


8-55 


42 




43 


42-21 


8-20 


42-17 


8-3 9 


42-14 


8-5 7 


42-10 


8-76 


43 




44 


43-19 


8-4o 


43-i5 


8-58 


43-12 


8-77 


43-08 


8.96 


44 




45 


44-17 


8-5 9 


44-14 


8.78 


44-io 


8-97 


44-o6 


9. 16 


45 




46 


45-i5 


8-7B 


45-12 


8.97 


45-o8 


9-17 


45-04 


0-37 


46 




47 


46-14 


8-97 


46-10 


9-17 


46-06 


9-37 


46-02 


9-57 


47 




48 


47-12 


9-16 


47- 08 


9-36 


47-o4 


9.57 


46-99 


9.78 


48 




i 9 


48-10 


9-35 


48-06 


9-56 


48-02 


9-77 


47-97 


9.98 


4 9 




5o 


49-08 


9-54 


49-o4 


9 . 7 5 


49-00 


9-97 


48-95 


10-18 


5o 




6 
o 

B 
5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


« 



B 
OS 

00 

a 




1 


9° 


78|° 


78 


i° 


78 


*° 





t 


















Table IV. 




TRAVERSE TABLE. 






109 


g 

3 


1] 


1° 


m 





1H° 


11 


1° 


g 

3 


• 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


5o-o6 


9.73 


5o-02 


9 . 9 5 


49-98 


10-17 


49-93 


10-39 


5i 


52 


5i-o4 


9-92 


5i-oo 


10-14 


5o- 


96 


10-37 


5o 


91 


10-59 


52 


53 


52 -o3 


IO-II 


5i- 9 8 


io-34 


5i 


94 


10-57 


5i 


89 


10-79 


53 


54 


53-oi 


io-3o 


52-96 


io-53 


52- 


92 


10-77 


52 


87 


11-00 


54 


55 


53 -99 


10-49 


53-94 


10-73 


53 


90 


10-97 


53 


85 


11-20 


55 


56 


54-97 


10-69 


54-92 


10-93 


54 


88 


ii-i6 


54 


83 


11 -4o 


56 


5 7 


55.95 


10-88 


55-90 


11-12 


55 


86 


u-36 


55 


81 


11-61 


5 1 


58 


56- 9 3 


11-07 


56 -89 


11-32 


56 


84 


n-56 


56 


78 


n-8i 


58 


5 9 


57-92 


11-26 


57-87 


11. 5i 


5 7 


82 


11 -76 


5 7 


76 


12-01 


5 9 


6o 


58- 9 o 


n-45 


58-85 


11-71 


58 


80 


11-96 


58 


74 


12-22 


60 


6i 


59-88 


11-64 


5 9 - 83 


11-90 


59 


78 


I2-l6 


5 9 


72 


12-42 


61 


62 


6o-86 


n-83 


6o-8i 


12-10 


60 


76 


12-36 


60 


70 


12-63 


62 


63 


61-84 


12-02 


61-79 


12-29 


61 


74 


12-56 


61 


68 


12-83 


63 


64 


62-82 


12-21 


62-77 


12-49 


62 


72 


12-76 


62 


66 


i3-o3 


64 


65 


63- 81 


12-40 


63- 7 5 


12-68 


63 


70 


12-96 


63 


64 


i3-24 


65 


66 


64-79 


12-59 


64-73 


12-88 


64 


68 


i3-i6 


64 


62 


i3-44 


66 


12 


65-77 


12.78 


65- 7 i 


i3-07 


65 


66 


i3-36 


65 


60 


i3-64 


67 


66-75 


12-98 


66-69 


i3-2 7 


66 


63 


i3-56 


66 


58 


i3-85 


68 


6 9 


67.73 


13.17 


67-67 


13-46 


67 


61 


13.76 


67 


55 


i4-o5 


69 


70 


68-71 


i3-36 


68-66 


i3-66 


68 


5 9 


13.96 


68 


53 


14-25 


70 


7i 


69-70 


13-55 


69-64 


i3-85 


69 


57 


14-16 


69 


5i 


14-46 


71 


72 


70-68 


i3- 7 4 


70-62 


i4-o5 


70 


55 


U-35 


70 


49 


U-66 


72 


73 


71-66 


i3- 9 3 


71-60 


14-24 


7i 


53 


14-55 


7i 


47 


14-87 


73 


74 


72-64 


I4-I2 


72-58 


14-44 


72 


5i 


14-75 


72 


45 


i5-07 


74 


75 


73-62 


i4-3i 


73-56 


14-63 


73 


49 


14-95 


73 


43 


i5-27 


75 


76 


74-60 


i'4-5o 


74-54 


14-83 


74 


47 


i5-i5 


74 


4i 


15-48 


76 


77 


75-59 


14-69 


75-52 


i5-o2 


75 


45 


i5-35 


75 


39 


15-68 


77 


78 


76-57 


14-88 


76 -5o 


l5-22 


76 


43 


i5-55 


76 


37 


15-88 


78 


22 


77-55 


i5-07 


77-48 


i5-4i 


77 


41 


15.75 


77 


34 


16-09 


79 


78.53 


15-26 


78-46 


i5-6i 


78 


3 9 


i5- 9 5 


78 


32 


16-29 


80 


81 


79. 5i 


15-46 


79'44 


i5-8o 


79 


37 


i6-i5 


79 


3o 


16-49 


81 


82 


80-49 


15-65 


80-42 


16-00 


80 


35 


i6-35 


80 


28 


16-70 


82 


83 


81-48 


15-84 


8i-4i 


16-19 


81 


33 


16.55 


81 


26 


16-90 


83 


84 


82.46 


i6-o3 


82-39 


i6-3 9 


82 


3i 


i6- 7 5 


82 


24 


17-11 


84 


85 


83-44 


16-22 


83-37 


i6-58 


83 


29 


i6- 9 5 


83 


22 


i 7 -3i 


85 


86 


84-42 


16-41 


84-35 


16-78 


84 


.27 


i 7 -i5 


84 


20 


i7-5i 


86 


87 


85-4o 


16-60 


85-33 


16.97 


85 


-25 


17-35 


85 


18 


17.72 


8 1 


88 


86-38 


16-79 


86-3i 


17-17 


86 


•23 


17-54 


86 


16 


17-92 


88 


89 


87-36 


16-98 


87-29 


17-36 


87 


•21 


17-74 


87 


14 


18. 12 


89 


90 


88-35 


17.17 


88-27 


17-56 


88 


19 


17-94 


88 


11 


i8-33 


90 


91 


89.33 


17-36 


89-25 


17.75 


89 


•17 


18-14 


89 


• 09 


18.53 


91 


92 


90- 3 1 


17.55 


90-23 


17.95 


90 


• i5 


18-34 


90 


07 


18-74 


92 


9 3 


91-29 


17.75 


91-21 


18-14 


9i 


•i3 


18-54 


9 1 


• o5 


18.94 


93 


9 i 


92-27 


17.94 


92-19 


18.34 


92 


11 


18.74 


92 


o3 


19-14 


94 


9 5 


g3 -25 


18. i3 


93-17 


18-53 


9 3 


• 09 


18-94 


9 3 


01 


i 9 -35 


9 5 


96 


94-24 


18.32 


94-16 


i8. 7 3 


94 


■ 07 


19-14 


9 3 


99 


19-55 


96 


9 l 


95-22 


18. 5i 


95-14 


18-92 


9 5 


■ o5 


19.34 


94 


•97 


19-75 


9 l 


98 


96-20 


18.70 


96-12 


19-12 


96 


•o3 


19-54 


95 


95 


19-96 


98 


99 


97-i8 


18-89 


97-10 


i9-3i 


97 


• 01 


19.74 


96 


93 


20-16 


99 


100 


98-16 


19.08 


98-08 


i9-5i 


97-99 


19-94 


97-90 


20-36 


100 


0) 



c 

5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


4) 

O 

a 

eS 

OQ 

5 


7< 


J° 


78 


1° 


78 


h° 


78 


i° 



110 






TRAVERSE TABLE. 




Table IV. 


(5 


12° 


12i° 


in° 


12 


1° 


g 

GO 

f» 

3 

ra 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


0-98 


0-21 


0-98 


0-21 


0-98 


0-22 


0-98 


0-22 


I 


2 


1 


96 


• 0-42 


1 


9 D 


0-42 


I-95 


0-43 


I 


9 5 


o-44 


2 


3 


2 


9 3 


0-62 


2 


9 3 


0-64 


2-93 


o-65 


2 


93 


o-66 


3 


4 


3 


9 1 


o-83 


3 


91 


o-85 


3-91 


0-87 


3 


90 


0-88 


4 


5 


4 


89 


1-04 


4 


89 


I- 06 


4-88 


1-08 


4 


88 


I -10 


5 


6 


5 


87 


1-25 


5 


86 


1-27 


5-86 


i>3o 


5 


85 


1-32 


6 


I 


6 


85 


1-46 


6 


84 


1-49 


6-83 


1-52 


6 


83 


1-54 


? 


7 


83 


1-66 


7 


82 


1-70 


7-81 


i. 7 3 


7 


80 


1-77 


9 


8 


80 


1 -87 


8 


80 


1.91 


8-79 


1 -95 


8 


78 


1.99 


9 


10 


9 


78 


2-08 


9 


77 


2-12 


9.76 


2-l6 


9 


7 5 


2-21 


10 


ii 


10 


76 


2-29 


10 


75 


2-33 


10-74 


2-38 


10 


73 


2-43 


11 


12 


11 


74 


2-49 


11 


73 


2-55 


11-72 


2-6o 


11 


70 


2-65 


12 


i3 


12 


72 


2-70 


12 


70 


2-76 


12-69 


2-8l 


12 


68 


2-87 


i3 


14 


i3 


69 


2-91 


i3 


68 


2-97 


13-67 


3-o3 


i3 


65 


3-09 


14 


i5 


14 


67 


3-12 


14 


66 


3-i8 


14-64 


3-25 


14 


63 


3-3i 


i5 


16 


i5 


65 


3-33 


i5 


64 


3-3 9 


l5-62 


3-46 


i5 


61 


3-53 


16 


n 


16 


63 


3-53 


16 


61 


3-6i 


16-60 


3-68 


16' 


58 


3-75 


17 


18 


17 


61 


3-74 


H 


59 


3-82- 


i7-5 7 


3-90 


17 


56 


3.97 


18 


*9 


18 


58 


3- 9 5 


18 


57 


4-o3 


iS-55 


4-n 


18 


53 


4-19 


19 


20 


19 


56 


4-16 


19 


54 


4-24 


19.53 


4-33 


19 


5i 


4-4i 


20 


21 


20 


54 


4-3 7 


20 


52 


4.46 


20-5o 


4-55 


20 


48 


4-63 


21 


22 


21 


52 


4-57 


21 


5o 


4-6 7 


21-48 


4-76 


21 


46 


4-86 


22 


23 


22 


5o 


4-78 


22 


48 


4-88 


22.45 


4.98 


22 


43 


5.o8 


23 


24 


23 


48 


4-99 


23 


45 


5-09 


23-43 


5-19 


23 


4i 


5-3o 


24 


25 


24 


45 


5-20 


24 


43 


5-3o 


24-41 


5-4i 


24 


38 


5-52 


25 


26 


25 


43 


5-4i 


23 


4i 


5-52 


25-38 


5-63 


25 


36 


5-74 


26 


27 


26 


4i 


5-6i 


26 


3 9 


5-73 


26-36 


5-84 


26 


33 


5.96 


27 


28 


27 


3 9 


5-82 


27 


36 


5-94 


27.34 


6-06 


27 


3i 


6-i8 


28 


29 


28 


37 


6-o3 


28 


34 


6-i5 


28- 3i 


6-28 


28 


28 


6-40 


29 


3o 


29 


34 


6-24 


29 


32 


6-37 


29-29 


6.49 


29 


26 


6-62 


3o 


3i 


3o 


32 


6-45 


3o 


29 


6-58 


30-27 


6.71 


3o 


24 


6-84 


3i 


32 


3i 


3o 


6-65 


3i 


27 


6-79 


3i-24 


6- 9 3 


3i 


21 


7. 06 


32 


33 


32 


28 


6-86 


32 


25 


7-00 


32-22 


7-U 


32 


'9 


7.28 


33 


34 


33 


26 


7-07 


33 


23 


7-21 


33.19 


7-36 


33 


16 


7-5o 


34 


35 


34 


24 


7-28 


34 


20 


7-43 


34-17 


7-58 


34 


14 


7-72 


35 


36 


35 


21 


7-48 


35 


18 


7-64 


35- 15 


7-79 


35 


11 


7-95 


36 


37 


36 


l 9 


7.69 


36 


16 


7-85 


36-12 


8-oi 


36 


09 


8.17 


37 


38 


37 


n 


7-9° 


37 


i3 


8-o6 


37-10 


8-22 


37 


06 


8-3 9 


38 


3 9 


38 


i5 


8-n 


38 


11 


8-27 


38-o8 


8-44 


38 


04 


8-6i 


39 


4o 


3 9 


i3 


8-32 


39 


09 


8.49 


39-o5 


8-66 


39 


01 


8-83 


40 


4i 


40 


10 


8-52 


4o 


07 


8.70 


40 -o3 


8-87 


3 9 


99 


9-o5 


4i 


42 


4i 


08 


8-73 


4i 


04 


8-91 


41 -oo 


9'°9 


40 


96 


9-27 


42 


43 


42 


06 


8.94 


42 


02 


9- 12 


41-98 


9-3i 


4t 


94 


9-49 


43 


44 


43 


04 


9-i5 


43 


00 


9-34 


42-96 


9.52 


42 


92 


9-71 


44 


45 


44 


02 


9-36 


43 


98 


9-55 


43-93 


9-74 


43 


89 


9 - 9 3 


45 


46 


44 


99 


9-56 


44 


9 5 


9-76 


44-qi 


9-96 


44 


87 


io-i5 


46 


47 


45 


97 


9-77 


45 


93 


9-97 


43-89 


10-17 


45 


84 


10-37 


47 


48 


46 


95 


9.98 


46 


9 1 


10-18 


46-86 


10-39 


46 


82 


10-59 


48 


4 9 


47 


93 


10-19 


47 


88 


io-4o 


47-84 


io-6i 


47 


79 


10-81 


49 


5o 


48-91 


io-4o 


48-86 


10-01 


48- 81 


10-82 


48-77 


11 -o3 


5o 


Distance. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




c 

5 
Q 


7 


3° 


77f° 


77 


4° 


77 


i° 



Table IV. 


TRAVERSE TABLE. 




Ill 


3 
O 
O 


12° 


V 


'1° 


12i° 


12|° 


3 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


49-89 


io- 60 


49-84 


10-82 


49-79 


II- 04 


49-74 


11-26 


5i 


52 


5o-86 


io-8i 


5o-82 


n-o3 


5o-77 


11-25 


50-72 


11-48 


52 


53 


5i-84 


11-02 


5i- 79 


11-25 


5i-74 


n-47 


5i -69 


11-70 


53 


54 


52-82 


11-23 


52.77 


11-46 


52-72 


11-69 


52-67 


11-92 


54 


55 


53- 80 


- n-44 


53- 7 5 


11-67 


53-70 


11-90 


53-64 


12-14 


55 


56 


54-78 


11-64 


54-72 


11.88 


54-67 


12-12 


54-62 


12-36 


56 


5 7 


55-75 


u.85 


55.70 


12.09 


55-65 


12-34 


55- 5 9 


12-58 


57 


58 


56- 7 3 


12-06 


56-68 


I2-3l 


56-63 


12-55 


56-57 


12-80 


58 


5 9 


57.71 


12-27 


57.66 


12-52 


57-60 


12-77 


57-55 


l3-02 


5 9 


6o 


58 -69 


12-47 


58-63 


I2-73 


58-58 


12-99 


58-52 


i3-24 


60 


6i 


59-67 


12-68 


59-61 


12-94 


5 9 -55 


l3-20 


59 -5o 


13-46 


61 


62 


6o- 65 


12-89 


60-59 


i3-i6 


6o-53 


i3-42 


60-47 


i3-68 


62 


63 


61 -62 


i3-io 


61-57 


l3-3 7 


61. 5i 


i3-64 


6i-45 


13.90 


63 


64 


62-60 


i3-3i 


62-54 


i3-58 


62-48 


i3-85 


62-42 


14-12 


64 


65 


63-58 


i3-5i 


63-52 


i3-79 


63-46 


14-07 


63-4o 


14-35 


65 


66 


64-56 


13-72 


64 -5o 


i4-oo 


64-44 


14-29 


64- 3 7 


14-57 


66 


67 


65-54 


i3 -93 


65-47 


14-22 


65-4i 


i4-5o 


65-35 


14-79 


67 


68 


66- 5i 


I4-I4 


66-45 


14-43 


66- 3 9 


14-72 


66-32 


i5-oi 


68 


69 


67.49 


14-35 


67-43 


14-64 


67-36 


14-93 


67-30 


i5-23 


69 


70 


68.47 


14-55 


68-41 


14-85 


68-34 


i5-i5 


68-27 


i5-45 


70 


7i 


69.45 


14-76 


69 -38 


i5-o6 


69-32 


i5-3 7 


69-25 


i5-6 7 


7i 


72 


70-43 


14-97 


70-36 


i5- 2 8 


70-29 


15-58 


70-22 


i5.8 9 


72 


73 


71-40 


i5-i8 


71-34 


15.49 


71-27 


i5-8o 


71-20 


16-11 


73 


74 


72-38 


i5 -39 


72-32 


15.70 


72-25 


16-02 


72-18 


i6.33 


74 


75 


73-36 


15.59 


73.29 


15.91 


73-22 


i6-23 


73-i5 


i6.55 


7 5 


76 


74-34 


i5-8o 


74-27 


16. i3 


74-20 


i6-45 


74-i3 


16.77 


76 


77 


7 5-32 


16-01 


75-25 


16.34 


75-17 


16-67 


75-io 


16.99 


77 


78 


76-30 


16-22 


76-22 


i6.55 


76-i5 


16-88 


76-08 


17.21 


78 


11 


77.27 


i6-43 


77-20 


16-76 


77. i3 


17-10 


77 -o5 


17-44 


79 


78-25 


16-63 


78-18 


16.97 


78-10 


17-32 


78-03 


17.66 


80 


81 


79-23 


16-84 


79-16 


17-19 


79.08 


17.53 


79-00 


17-88 


81 


82 


80-21 


i7-o5 


8o-i3 


17.40 


80-06 


17-75 


79-98 


i8- 10' 


82 


83 


81.19 


17-26 


8i- 11 


17-61 


8i- o3 


17-96 


8o- 9 5 


i8-32 


83 


84 


82.16 


17-46 


82-09 


17-82 


82-01 


18. 18 


8i- 9 3 


18.54 


84 


85 


83-14 


17.67 


83- 06 


18-04 


82-99 


18-40 


82-90 


18-76 


85 


86 


84-12 


17-88 


84-04 


18. 25 


83 -96 


18-61 


83-88 


18-98 


86 


11 


85-10 


18-09 


85-02 


18.46 


84-94 


i8-83 


84-85 


19-20 


87 


86-o8 


i8-3o 


86-oo 


18-67 


85- 9 i 


19-05 


85-83 


19-42 


88 


89 


87.06 


i8-5o 


86.97 


18.88 


86-89 


19-26 


86-8i 


19.64 


89 


90 


88- o3 


18-71 


87.95 


19-10 


87.87 


19-48 


87-78 


19-86 


90 


9 1 


89-01 


18-92 


88- 9 3 


19.31 


88-84 


19-70 


88-76 


20- 08 


9 1 


92 


89.99 


19-13 


89-91 


19.52 


89-82 


19-91 


89-73 


20-3o 


9? 


9 3 


90-97 


19-34 


90-88 


19.73 


90-80 


20-l3 


90-71 


20-52 


9 3 


9| 


9 i- 9 5 


19-54 


91-86 


I9-94 


9 J -77 


20-35 


91-68 


20-73 


94 


9 5 


92-92 


19.75 


92-84 


20-l6 


92-75 


20-56 


92-66 


20-97 


9 5 


96 


93.90 


19-96 


9 3-8i 


2?o-37 


93.72 


20-78 


9 3- 63 


21-19 


96 


97 


94-88 


20-17 


94-79 


20-58 


94-70 


20 .99 


94-61 


2I-4I 


97 


98 


9 5-86 


20-38 


93-77 


20-79 


9 5- 68 


21-21 


9 5- 58 


21-63 


98 


99 


96-84 


20-58 


96-75 


21-01 


96-65 


21-43 


96- 56 


21-85 


99 


100 


97.81 


20-79 


97-72 


21-22 


97-63 


21-64 


97-53 


22-07 


100 




c 

rt 

V} 

3 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 


a 
a 

1 ' 


78° 


11 


30 

1 


11h° 


m° 



112 






TRAVERSE TABLE. 




Table IV. 


o 

s 
o 
a 


13° 


18*° 


13*° 


13|° 


3 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


0.97 


o-23 


0-97 


0-23 


0-97 


0-23 


0-97 


0-24 


I 


2 


I- 


9 5 


0- 


45 


I- 


9 5 


0-46 


I- 


9 5 





47 


1 


94 


0- 


48 


2 


3 


2- 


92 


0- 


67 


2 


92 


0-69 


2- 


92 





70 


2 


01 





71 


3 


4 


3- 


90 


0- 


90 


3- 


89 


0-92 


3 


89 





9 3 


3 


89 





9 5 


4 


5 


4- 


ll 


I- 


12 


4- 


87 


i-i5 


4 


86 


1 


J 7 


4 


86 


1 


3 


5 


6 


5- 


I- 


35 


5 


84 


1-38 


5 


83 


1 


40 


5 


83 


1 


6 


I 


6- 


82 


I- 


5 7 


6 


81 


i- 60 


6 


81 


1 


63 


6 


80 


1 


66 


I 


7- 


80 


I- 


80 


7 


79 


1-83 


7 


78 


1 


87 


7 


77 


1 


90 


9 


8 


77 


2- 


02 


8 


76 


2-06 


8 


7 5 


2 


10 


8 


74 


2 


14 


9 


10 


9 


74 


2- 


25 


9 


73 


2-29 


9 


72 


2 


33 


9 


7i 


2 


38 


10 


ii 


10 


72 


2 


47 


10 


7i 


2-52 


10 


70 


2 


57 


10 


68 


2 


61 


11 


12 


11 


69 


2 


70 


11 


68 


2-75 


11 


67 


2 


80 


11 


66 


2 


85 


12 


i3 


12 


67 


2 


92 


12 


65 


2-98 


12 


64 


3 


o3 


12 


63 


3 


09 


i3 


14 


i3 


64 


3 


i5 


i3 


63 


3-21 


i3 


61 


3 


27 


i3 


60 


3 


33 


14 


i5 


14 


62 


3 


37 


14 


60 


3-44 


14 


5 9 


3 


5o 


14 


57 


3 


57 


i5 


16 


i5 


5 9 


3 


60 


i5 


u 


3-67 


i5 


56 


3 


74 


i5 


54 


3 


80 


16 


17 


16 


5 7 


3 


82 


16 


3-90 


16 


53 


3 


97 


16 


5i 


4 


04 


IS 


18 


l l 


54 


4 


o5 


n 


52 


4-i3 


17 


5o 


4 


20 


17 


48 


4 


.28 


!9 


18 


5i 


4 


27 


18 


49 


4-35 


18 


-48 


4 


44 


18 


-46 


4 


52 


19 


20 


19 


49 


4 


5o 


19 


47 


4-58 


19 


45 


4 


.67 


19 


-43 


4 


75 


20 


21 


20 


46 


4 


72 


20 


44 


4-8i 


20 


■42 


4 


.90 


20 


• 40 


4 


'99 


21 


22 


21 


44 


4 


9 5 


21 


4i 


5-o4 


21 


• 3 9 


5 


•14 


21 


•37 


5 


■23 


22 


23 


22 


41 


5 


17 


22 


39 


5-27 


22 


-36 


5 


• 3 7 


22 


-34 


5 


•47 


23 


24 


23 


38 


5 


40 


23 


36 


5-5o 


23 


-34 


5 


• 6o 


23 


-3i 


5 


■ 70 


24 


25 


24 


36 


5 


62 


24 


33 


5- 7 3 


24 


• 3i 


5 


• 84 


24 


-28 


5 


•94 


25 


26 


25 


33 


5 


85 


25 


3i 


5-96 


25 


• 28 


6 


• 07 


25 


-25 


6 


.18 


26 


27 


26 


3i 


6 


07 


26 


28 


6- 19 


26 


-25 


6 


• 3o 


26 


•23 


6 


•42 


ll 


28 


27 


28 


6 


3o 


27 


25 


6-42 


27 


•23 


6 


•54 


27 


•20 


6 


■ 66 


29 


28 


26 


6 


52 


28 


23 


6-65 


28 


20 


6 


■77 


28 


17 


6 


89 


29 


3o 


29 


23 


6 


7 5 


29 


20 


6-88 


29 


*7 


7 


00 


29 


14 


7 


i3 


3o 


3i 


3o 


21 


6 


97 


3o 


n 


7-u 


3o 


14 


7 


24 


3o 


■II 


7 


37 


3i 


32 


3i 


18 


7 


20 


3i 


i5 


7-33 


3i 


12 


7 


47 


3i 


•08 


7 


61 


32 


33 


32 


i5 


7 


42 


32 


12 


7-56 


32 


09 


7 


■ 70 


32 


• o5 


7 


■ 84 


33 


34 


33 


i3 


7 


65 


33 


09 


7-79 


33 


06 


7 


•94 


33 


• o3 


8 


.08 


34 


35 


34 


10 


7 


87 


34 


07 


8-02 


34 


o3 


8 


n 


34 


•00 


8 


•32 


35 


36 


35 


08 


8 


10 


35 


04 


8-25 


35 


01 


8 


•40 


34 


•97 


8 


• 56 


36 


37 


36 


o5 


8 


32 


36 


02 


8-48 


35 


■98 


8 


-64 


35 


•94 


8 


•79 


37 


38 


37 


o3 


8 


55 


36 


99 


8-71 


36 


-95 


8 


87 


36 


•9* 


9 


•o3 


38 


3 9 


38 


00 


8 


77 


37 


9 6 


8- 9 4 


37 


"S 2 


9 


•10 


37 


• 88 


9 


• 27 


39 


4o 


38 


97 


9 


00 


38 


94 


9-17 


38 


.89 


9 


34 


38 


-85 


9 


• 5i 


4o 


41 


3 9 


9 5 


9 


22 


3 9 


9 1 


9-4o 


39 


•87 


9 


57 


3 9 


• 83 


9 


75 


4i 


42 


4o 


92 


9 


45 


4o 


88 


9-63 


40 


84 


9 


•80 


4o 


• 8o 


9 


98 


42 


43 


4i 


00 


9 


67 


41 


86 


9-86 


4i 


81 


10 


•04 


4i 


■77 


10 


• 22 


43 


44 


42 


• 87 


9 


90 


42 


83 


io- 08 


42 


.78 


10 


.27 


42 


■74 


10 


46 


44 


45 


43 


•85 


10 


12 


43 


• 80 


io-3i 


43 


.76 


10 


■ 5i 


43 


•7i 


10 


70 


45 


46 


44 


•82 


10 


35 


44 


.78 


io-54 


44 


73 


10 


■74 


44 


• 68 


10 


93 


46 


47 


45 


•80 


10 


57 


45 


•75 


10-77 


45 


70 


10 


97 


45 


•65 


11 


17 


47 


48 


46 


•77 


10 


■80 


46 


■72 


11-00 


46 


.67 


11 


•21 


46 


• 62 


11 


4i 


48 


49 


47 


•74 


11 


•02 


47 


■ 70 


11-23 


47 


• 65 


11 


44 


47 


-6o 


11 


65 


i 9 


5o 


48-72 


11-25 


48-67 


n-46 


48-62 


11-67 


48-5 7 


n-88 


5o 


CO 

a 

a 
a 

5 


Dep. 


Lat. 


Dep. 


Lat. . 


Dep. 


Lat. 


Dep. 


Lat. 


a 
tt 

to 
















1 


1° 


76|° 


16£° 


76 


4° 





Table IV. 




TRAVERSE TABLE. 




113 


e 

55' 

3 
o 
3 


13° 


134° 


13i° 


1"30 
ID j 


a 

a 

CD 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


49-69 


u-47 


49-64 


II.69 


49-59 


11 91 


49-54 


12-12 


5i 


52 


5o-67 


11-70 


5o-62 


II 


92 


5o 


56 


12 


14 


5o 


5i 


12 


36 


52 


53 


5i-64 


11.92 


5i -59 


I2> 


i5 


5i 


54 


12 


37 


5i 


48 


12 


60 


53 


54 


52-62 


12-l5 


52-56 


12 


38 


52 


5i 


12 


61 


52 


45 


12 


84 


54 


55 


53.5q 


12.37 


53-54 


12 


61 


53 


48 


12 


84 


53 


42 


13 


07 


55 


56 


54-56 


12 -6o 


54-5i 


12 


84 


54 


45 


i3 


07 


54 


40 


13 


3i 


56 


57 


55-54 


12-82 


55-48 


i3 


06 


55 


43 


i3 


3i 


55 


37 


13 


55 


5 7 


58 


56-5i 


i3-o5 


56-46 


i3 


29 


56 


40 


i3 


54 


56 


34 


i3 


79 


58 


5 9 


57-49 


i3-27 


57-43 


i3 


52 


57 


37 


i3 


77 


5 7 


3i 


14 


02 


5 9 


6o 


58-46 


i3-5o 


58-40 


i3 


75 


58 


34 


14 


01 


58 


28 


14 


26 


60 


6i 


5 9 -44 


13.72 


5 9 -38 


i3 


98 


59 


3i 


14 


24 


5 9 


25 


14 


5o 


6i 


62 


6o-4i 


13.95 


60 -35 


14 


21 


60 


29 


14 


47 


60 


22 


14 


74 


62 


63 


61 -39 


14-17 


6i-32 


14 


44 


61 


26 


14 


7i 


61 


J 9 


14 


97 


63 


64 


62-36 


14-40 


62- 3o 


14 


67 


62 


23 


14 


94 


62 


l l 


i5 


21 


64 


65 


63-33 


14-62 


63.27 


14 


90 


63 


20 


i5 


H 


63 


14 


i5 


45 


65 


66 


64-3i 


14-85 


64-24 


IS 


i3 


64 


18 


i5 


4i 


64 


11 


i5 


6 ? 


66 


& 


65-28 


i5-07 


65-22 


i5 


36 


65 


i5 


i5 


64 


65 


08 


i5 


93 


67 


66-26 


i5-3o 


66-19 


i5 


5 9 


66 


12 


i5 


87 


66 


o5 


16 


16 


68 


6 9 


67.23 


15-52 


67-16 


i5 


81 


67 


09 


16 


11 


67 


02 


16 


40 


69 


70 


68-21 


15.75 


68.14 


16 


04 


68 


07 


16 


34 


67 


99 


16 


64 


70 


7i 


69.18 


15.97 


69-11 


16 


27 


69 


04 


16 


5 7 


68 


97 


16 


88 


7i 


72 


70. i5 


16-20 


70-08 


16 


5o 


70 


01 


16 


81 


69 


94 


17 


11 


72 


73 


71 • i3 


16-42 


71-06 


16 


73 


70 


98 


17 


04 


70 


91 


n 


35 


73 


74 


72-10 


16-65 


72-o3 


16 


96 


7i 


96 


17 


28 


7i 


88 


n 


5 9 


74 


75 


73-o8 


16-87 


73-00 


n 


J 9 


72 


93 


n 


5o 


72 


85 


n 


83 


75 


76 


74-o5 


17.10 


73.98 


17 


42 


73 


90 


17 


74 


73 


82 


18 


06 


76 





75-o3 


17-32 


74-95 


17 


65 


74 


87 


17 


98 


74 


79 


18 


3o 


7 2 


76-00 


17.55 


75.92 


17 


88 


75 


84 


18 


21 


75 


76 


18 


54 


78 


29 


76-98 


17-77 


76-00 


18 


11 


76 


82 


18 


44 


76 


74 


18 


78 


I 9 


80 


77.95 


18-00 


77.87 


18 


34 


77 


79 


18 


68 


77 


7i 


19 


01 


80 


81 


78-92 


18-22 


78-84 


18 


57 


78 


76 


18 


91 


78 


68 


19 


25 


81 


82 


79.90 


18.45 


79-82 


18 


79 


79 


73 


19 


14 


79 


65 


J 9 


49 


82 


83 


80-87 


18-67 


80-79 


J 9 


02 


80 


71 


19 


38 


80 


62 


19 


•73 


83 


84 


8i- 85 


18-90 


81-76 


19 


25 


81 


68 


19 


61 


81 


-5 9 


19 


97 


84 


85 


82-82 


19. 12 


82-74 


l 9 


• 48 


82 


65 


J 9 


84 


82 


• 56 


20 


20 


85 


86 


83- 80 


19.35 


83-71 


*9 


•7 1 


83 


62 


20 


08 


83 


•54 


20 


44 


86 


ll 


84-77 


19-57 


84-68 


19 


.94 


84 


60 


20 


3i 


84 


■ 5i 


20 


■ 68 


87 


85-74 


19-80 


85-66 


20 


• J 7 


85 


■57 


20 


54 


85 


48 


20 


.92 


88 


89 


86.72 


20-02 


86-63 


20 


•40 


86 


•54 


20 


78 


86 


• 45 


21 


i5 


89 


90 


87-69 


20-20 


87-60 


20 


-63 


87 


• 5i 


21 


01 


87 


•42 


21 


3 9 


90 


9 1 


88-67 


20-47 


88-58 


20 


• 86 


88 


•49 


21 


24 


88 


• 3 9 


21 


63 


9i 


92 


89-64 


20.70 


89.55 


21 


• 09 


89 


• 46 


21 


48 


89 


• 36 


21 


87 


92 


9 3 


90-62 


20-92 


90.52 


21 


•32 


90 


• 43 


21 


71 


90 


• 33 


22 


10 


9 3 


94 


91-59 


2I-l5 


91 -5o 


21 


•54 


9 1 


.40 


21 


94 


9 1 


3i 


22 


34 


9 i 


95 


92-57 


21.37 


92-47 


21 


•77 


92 


■38 


22 


18 


92 


28 


22 


58 


9 5 


96 


93-54 


21 -6o 


93-44 


22 


• 00 


93 


• 35 


22 


4r 


9 3 


25 


22 


82 


96 


9 


94 -5i 


21-82 


94-42 


22 


•23 


94 


•32 


22 


64 


94 


22 


23 


06 


9 l 


95-49 


22-05 


95-39 


22 


-46 


95 


.29 


22 


88 


9 2 


19 


23 


29 


98 


99 


96-46 


22-27 


96- 36 


22 


.69 


96 


.26 


23 


11 


96 


16 


23 


53 


99 


100 


97-44 


22-50 


97-34 


22 


.92 


97-24 


23-34 


97-i3 


23-77 


100 


6 


a 
3 

CO 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


a 

1 


7 


7° 


76|° 


76£° 


76i° 

























114 






TRAVERSE TABLE, 




Table IV. 




@ 

A 

CD 


14° 


144° 


U£° 


14 


1° 


| 

p 

C5 
CD 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




I 


97 


0-24 


97 


0-25 


97 


0-25 


0-97 


0-25 


I 




2 


I 


94 


0-48 


1 


94 


0-49 


1 


94 





5o 


1 


9 3 


o-5i 


2 




3 


2 


91 


0-73 


2 


91 


0-74 


2 


90 





75 


2 


90 


0-76 


3 




4 


3 


88 


0-97 


3 


88 


0-98 


3 


87 


1 


00 


3 


87 


1-02 


4 




5 


4 


85 


I-2I 


4 


85 


1-23 


4 


84 


1 


25 


4 


84 


1-27 


5 




6 


5 


82 


1-45 


5 


82 


1.48 


5 


81 


1 


5o 


5 


80 


i-53 


6 




7 


6 


79 


1-69 


6 


78 


1-72 


6 


78 


1 


75 


6 


77 


1-78 


7 




8 


7 


76 


1-94 


7 


75 


1-97 


7 


7 5 


2 


00 


7 


74 


2-04 


8 




9 


8 


73 


2-18 


8 


72 


2-22 


8 


71 


2 


25 


8 


70 


2-29 


9 




10 


9 


70 


2«42 


9 


69 


2-46 


9 


68 


2 


5o 


9 


67 


2-55 


10 




ii 


10 


67 


2-66 


10 


66 


2-71 


10 


65 


2 


75 


10 


64 


2-80 


11 




12 


11 


64 


2-90 


11 


63 


2-95 


11 


62 


3 


00 


11 


60 


3-o6 


12 




i3 


12 


61 


3-i5 


12 


60 


3-20 


12 


59 


3 


25 


12 


57 


3-3i 


i3 




14 


i3 


58 


3-3 9 


i3 


57 


3-45 


i3 


55 


3 


5i 


i3 


54 


3-56 


14 




i5 


14 


55 


3-63 


14 


54 


3-69 


14 


52 


3 


76 


14 


5i 


3-82 


i5 




16 


i5 


52 


3-87 


i5 


5i 


3- 9 4 


i5 


49 


4 


01 


i5 


47 


4-07 


16 




17 


16 


5o 


4-u 


16 


48 


4-i8 


16 


46 


4 


26 


16 


•44 


4-33 


n 




18 


17 


47 


4-35 


n 


45 


4-43 


17 


•43 


4 


5i 


17 


4i 


4-58 


18 




19 


18 


44 


4-6o 


18 


42 


4-68 


18 


39 


4 


76 


18 


•37 


4-84 


*9 




20 


*9 


4i 


4.84 


19 


38 


4-92 


l 9 


36 


5 


01 


J 9 


34 


5-09 


20 




21 


20 


38 


5-o8 


20 


35 


5-i 7 


20 


33 


5 


.26 


20 


•3i 


5-35 


21 




22 


21 


35 


5-32 


21 


32 


5-42 


21 


3o 


5 


5i 


21 


.28 


5-6o 


22 




23 


22 


32 


5-56 


22 


29 


5-66 


22 


27 


5 


76 


22 


•24 


5-86 


23 




24 


23 


29 


5-8i 


23 


26 


5-91 


23 


24 


6 


01 


23 


■21 


6-n 


24 




25 


24 


26 


6-o5 


24 


23 


6-i5 


24 


20 


6 


26 


24 


18 


6-3 7 


25 




26 


2D 


23 


6-29 


25 


20 


6-4o 


25 


I? 


6 


5i 


25 


14 


6-62 


26 




27 


26 


20 


6-53 


26 


n 


6-65 


26 


14 


6 


76 


26 


11 


6-87 


27 




28 


27 


n 


6.77 


27 


14 


6-89 


27 


11 


7 


01 


27 


08 


7 -i3 


28 




29 


28 


14 


7-02 


28 


11 


7-i4 


28 


08 


7 


26 


28 


04 


7-38 


29 




3o 


29 


11 


7-26 


29 


08 


7-38 


29 


04 


7 


5i 


29 


01 


7-64 


3o 




3i 


3o 


08 


7-5o 


3o 


o5 


7-63 


3o 


01 


7 


76 


29 


98 


7-89 


3i 




32 


3i 


o5 


7-74 


3i 


02 


7-88 


3o 


98 


8 


01 


3o 


9 5 


8-i5 


32 




33 


32 


02 


7.98 


3i 


98 


8-12 


3i 


95 


8 


26 


3i 


91 


8.40 


33 




34 


32 


99 


8-23 


32 


9 5 


8-37 


32 


92 


8 


5i 


32 


88 


8-66 


34 




35 


33 


96 


8-47 


33 


92 


8-62 


33 


89 


8 


76 


33 


85 


8-91 


35 




36 


34 


9 3 


8.71 


34 


89 


8-86 


34 


85 


9 


01 


34 


81 


9-17 


36 




37 


35 


90 


8- 9 5 


35 


86 


9-n 


35 


82 


9 


26 


35 


78 


9-42 


37 




38 


36 


87 


9-19 


36 


83 


9-35 


36 


79 


9 


5i 


36 


7 5 


9-67 


38 




3 9 


37 


84 


9.44 


37 


80 


9-60 


37 


76 


9 


76 


37 


7i 


9'9 3 


39 




4o 


38' 


81 


9-68 


38 


77 


9-85 


38 


73 


10 


02 


38 


68 


10-18 


40 




4i 


3 9 


78 


9-92 


3 9 


74 


10-09 


39 


69 


10 


27 


39 


65 


10-44 


41 




42 


4o 


75 


10-16 


4o 


71 


io-34 


4o 


66 


10 


52 


40 


62 


10-69 


42 




43 


4i 


72 


10-40 


4i 


68 


io-58 


4i 


63 


10 


77 


41 


58 


10-95 


43 




44 


42 


69 


10-64 


42 


65 


io-83 


42 


60 


11 


02 


42 


55 


11-20 


44 




45 


43 


66 


10-89 


43 


62 


11-08 


43 


57 


11 


27 


43 


52 


11-46 


45 




46 


44 


63 


ii-i3 


44 


58 


11-32 


44 


53 


11 


52 


44 


48 


11-71 


46 




47 


45 


60 


11-37 


45 


55 


11-57 


45 


5o 


11 


77 


45 


45 


n-97 


47 




48 


46 


5 7 


ii-6i 


46 


52 


11-82 


46 


47 


12 


02 


46 


42 


12-22 


48 




i 9 


47 


54 


n-85 


47 


49 


12 -06 


47 


44 


12 


27 


47- 


3q 


12-48 


49 




5o 


48-01 


12-10 


48-46 


I2-3l 


48-41 


12-52 


48-35 


12-73 


5o 




O 

C 

a 

w 

S 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


O 

a 
a 

s 




7 


5° 


75 


10 
4 


75 


i° 


75 


1 





Table IV. 




TRAVERSE TABLE. 




115 


g 

3 
a 

.? 


14° 


14i° 


Ui° 


14f° 


a 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


49.49 


12-34 


49-43 


12-55 


49-38 


12.77 


4 9 -32 


I2- 9 8 


5i 


52 


5o-46 


12 


58 


5o 


40 


12-80 


5o 


34 


l3-02 


5o 


29 


i3-24 


52 


53 


5i-43 


12 


82 


5i 


37 


i3-o5 


5i 


3i 


i3-27 


5i 


25 


13-49 


53 


54 


52-4o 


13 


06 


52 


34 


i3-29 


52 


28 


13-52 


52 


22 


13.75 


54 


55 


53.37 


i3 


3i 


53 


3i 


13-54 


53 


25 


i3-77 


53 


19 


i4-oo 


55 


56 


54-34 


i3 


55 


54 


28 


13-78 


54 


22 


14-02 


54 


id 


14-26 


56 


5 7 


55-3i 


i3 


79 


55 


25 


i4-o3 


55 


18 


14-27 


55 


12 


i4-5i 


5 7 


58 


56-28 


14 


o3 


56 


'22 


14-28 


56 


i5 


14-52 


56 


09 


14-77 


58 


5 9 


57-25 


14 


27 


57 


18 


14-52 


57 


12 


14-77 


5 7 


06 


l5-02 


5 9 


6o 


58-22 


14- 


52 


58 


i5 


14-77 


58 


09 


l5-02 


58 


02 


15.28 


60 


6i 


59-19 


14- 


76 


5 9 


12 


l5-02 


59 


06 


i5-27 


58 


99 


15.53 


61 


62 


60-16 


i5- 


00 


60 


09 


15.26 


60 


o3 


i5-52 


5 9 


96 


i5-79 


62 


63 


6i- 13 


i5- 


24 


61 


06 


i5-5i 


60 


99 


i5-77 


60 


92 


16-04 


63 


64 


62-10 


i5- 


48 


62 


o3 


i5-75 


61 


9 6 


16-02 


61 


89 


16-29 


64 


65 


63-07 


i5- 


72 


63 


00 


16-00 


62 


93 


16-27 


62 


86 


i6.55 


65 


66 


64-04 


i5 


97 


63 


97 


i6-25 


63 


90 


16.53 


63 


83 


16-80 


66 


67 


65-oi 


16. 


3i 


64 


94 


16.49 


64 


87 


J6.78 


64 


79 


17-06 


67 


68 


65- 98 


16 


45 


65 


91 1 16-74 


65 


83 


i7-o3 


65 


76 


i 7 .3i 


68 


69 


66- 9 5 


16 


69 


66 


88 


16-98 


66 


80 


17.28 


66 


73 


17-57 


69 


70 


67-92 


16 


93 


67 


85 


17-23 


67 


77 


17.53 


67 


69 


17-82 


70 


7i 


68-89 


1.7" 


18 


68 


82 


17-48 


68 


74 


17.78 


68 


66 


18-08 


71 


72 


69-86 


n- 


42 


69 


78 


17-72 


69 


7i 


18. o3 


69 


63 


i8-33 


72 


73 


70-83 


n 


66 


70 


75 


17-97 


70 


67 


18-28 


70 


5 9 


i8-5g 


73 


H 


71-80 


n 


90 


7i 


72 


18-22 


7i 


64 


i8.53 


7i 


56 


18-84 


74 


75 


72-77 


18 


14 


72 


69 


18-46 


72 


61. 


18-78 


72 


53 


19- 10 


7 5 


7 6 


73-74 


18 


3 9 


73 


66 


18-71 


73 


58 


19 -o3 


73 


5o 


19-35 


76 


77 


74-71 


18 


63 


74 


63 


18-95 


74 


55 


19-28 


74 


46 


10-60 


77 


78 


75-68 


18 


87 


75 


60 


19-20 


75 


52 


19.53 


7 5 


43 


19-86 


78 


V 


76-65 


J 9 


11 


76 


5 7 


19-45 


76 


48 


19.78 


76 


4o 


20-11 


79 


80 


77-62 


*9 


35 


77 


54 


19-69 


77 


45 


20 -o3 


77 


36 


20-37 


80 


81 


78.59 


*9 


60 


73 


5i 


I9-94 


78 


42 


20-28 


78 


33 


20-62 


81 


82 


79. 56 


l 9 


84 


79 


48 


20-18 


79 


39 


20-53 


79 


3o 


20-88 


82 


83 


80 -53 


20 


08 


80 


45 


20-43 


80 


36 


20-78 


80 


26 


2I-l3 


83 


84 


81 • 5o 


20 


32 


81 


42 


20-68 


81 


32 


21-03 


81 


23 


21 -3 9 


84 


85 


82-48 


20 


56 


82 


38 


20-92 


82 


29 


21-28 


82 


20 


21-64 


85 


86 


83-45 


20 


81 


83 


35 


21-17 


83 


26 


21-53 


83 


17 


21-90 


86 


87 


84-42 


21 


o5 


84 


32 


21-42 


84 


23 


21-78 


84 


i3 


22-l5 


87 


88 


85- 3 9 


21 


29 


85 


29 


21-66 


85 


20 


22-03 


85 


10 


22-41 


88 


89 


86-36 


21 


53 


86 


26 


21 .91 


86 


n 


22-28 


86 


07 


22-66 


89 


90 


87-33 


21 


77 


87 


23 


22-l5 


87 


i3 


22-53 


87 


o3 


22-9I 


90 


9 1 


88- 3o 


22 


01 


88 


20 


22-40 


88 


10 


22-78 


88 


00 


23-17 


9 1 


9 l 


89-27 


22 


26 


89 


17 


22-65 


89 


07 


23-o4 


88 


97. 


23-42 


92 


9 3 


90-24 


22 


5o 


90 


14 


22-89 


90 


04 


23-29 


89 


94 


23-68 


9 3 


94 


91 -21 


22 


74 


91 


II 


23-14 


9 1 


01 


23-54 


90 


9° 


23-93 


94 


9 5 


92-l8 


22 


98 


92 


08 


23-38 


9 1 


97 


23.79 


9 1 


87 


24-19 


95 


96 


93. 1 5 


23 


22 


93 


•o5 


23-63 


92 


94 


24-04 


92 


84 


24-44 


96 


9 Z 


94-12 


23 


■47 


94 


■02 


23-88 


93 


9 1 


24-29 


9 3 


80 


24-70 


97 


98 


95-09 


23 


•71 


94 


.98 


24-12 


94 


88 


24-54 


94 


77 


24-9 5 


98 


99 


96-06 


23 


9 5 


9 5 


■ o5 


24-37 


9 5 


85 


24-79 


9 5 


74 


20-21 


99 


100 


97 -o3 


24-19 


96-92 


24-62 


96-81 


25-o4 


96-70 


25.46 


100 




Dep. 


Lat. 


Dep. 


Lat. 

' 


Dep. 


Lat. 


Dep. 


Lat. 


03 

s 


7 


3° 


75|° 


75i° 


754° 






















"^^ 














i 


















116 






TRAVERSE TABLE. 




Table IV. 


e 

p 

3 
CD 


15° 


15i° 


15i° 


15 


1° 


g 

a 

a 

a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


0.97 


0-26 


0-96 


0-26 


0-96 


0-27 


0-96 


0-27 


I 


2 


I 


9 3 





52 


1 


o3 





53 


I- 


s 3 





53 


I 


92 





54 


2 


3 


2 


90 





78 


2 


89 





79 


2 


89 





80 


2 


e2 





81 


3 


4 


3 


86 


1 


04 


3 


86 


I 


o5 


3 


85 


I 


07 


3 


1 


09 


4 


5 


4 


83 


1 


29 


4 


82 


I 


32 


4 


82 


I 


34 


4 


8l 


1 


36 


5 


6 


5 


80 


1 


55 


5 


79 


I 


58 


5 


78 


I 


60 


5 


77 


1 


63 


6 


3 


6 


76 


1 


81 


6 


7 5 


I 


84 


6 


75 


I 


87 


6 


74 


1 


90 


I 


i 


73 


2 


07 


7 


72 


2 


10 


7 


7i 


2 


14 


7 


70 


2 


n 


9 


69 


2 


33 


8 


68 


2 


37 


8 


67 


2 


4i 


8 


66 


2 


44 


9 


10 


9 


66 


2 


5 9 


9 


65 


2 


63 


9 


64 


2 


67 


9 


62 


2 


7i 


10 


ii 


10 


63 





85 


10 


61 


2 


89 


10 


60 


2 


94 


10 


5 9 


2 


99 


11 


12 


ii 


5 9 


3 


11 


11 


58 


3 


16 


11 


56 


3 


21 


11 


55 


3 


26 


12 


i3 


12 


56 


3 


36 


12 


54 


3 


42 


12 


53 


3 


47 


12 


5i 


3 


53 


i3 


i4 


i3 


52 


3 


62 


i3 


5i 


3 


68 


i3 


49 


3 


74 


i3 


47 


3 


80 


14 


i5 


14 


49 


3 


88 


14 


47 


3 


9 5 


14 


45 


4 


01 


14 


44 


4 


°7 


i5 


16 


i5 


43 


4 


14 


i5 


44 


4 


21 


i5 


42 


4 


28 


i5 


40 


4 


34 


16 


\l 


16 


42 


4 


40 


16 


4o 


4 


47 


16 


38 


4 


54 


16 


36 


4 


61 


17 


n 


3 9 


4 


66 


H 


37 


4 


73 


n 


35 


4 


81 


17 


32 


4 


89 


18 


l 9 


18 


35 


4 


92 


18 


33 


5 


00 


18 


3i 


5 


08 


18 


29 


5 


16 


l 9 


20 


19 


32 


5 


18 


19 


3o 


5 


26 


l 9 


27 


5 


34 


1$ 


2D 


5 


43 


20 


21 


20 


28 


5 


44 


20 


26 


5 


52 


20 


24 


5 


61 


20 


21 


5 


70 


21 


22 


21 


25 


5 


69 


21 


23 


5 


79 


21 


20 


5 


88 


21 


17 


5 


97 


22 


23 


22 


22 


5 


9 5 


22 


*9 


6 


00 


22 


16 


6 


■i5 


22 


•14 


6 


24 


23 


24 


23 


18 


6 


21 


23 


i5 


6 


3i 


23 


•i3 


6 


4i 


23 


•10 


6 


5i 


24 


25 


24 


i5 


6 


47 


24 


12 


6 


58 


24 


09 


6 


68 


24 


06 


6 


79 


25 


26 


25 


11 


6 


73 


25 


08 


6 


84 


25 


-o5 


6 


9 5 


25 


02 


7 


06 


26 


27 


26 


08 


6 


99 


26 


o5 


7 


10 


26 


02 


7 


22 


25 


99 


7 


33 


3 


28 


27 


o5 


7 


20 


27 


01 


7 


36 


26 


98 


7 


48 


26 


9 5 


7 


60 


29 


28 


01 


7 


5i 


27 


98 


7 


63 


27 


9 5 


I 


7 5 


27 


91 


7 


87 


29 


3o 


28 


98 


7 


76 


28 


94 


7 


89 


28 


91 


02 


28 


87 


8 


14 


3o 


3i 


29 


94 


8 


02 


29 


91 


8 


i5 


29 


87 


8 


28 


29 


84 


8 


4i 


3i 


32 


3o 


91 


8 


28 


3o 


87 


8 


42 


3o 


84 


8 


55 


3o 


80 


8 


69 


32 


33 


3i 


88 


8 


54 


3i 


84 


8 


68 


3i 


80 


8 


82 


3i 


76 


8 


96 


33 


34 


32 


84 


8 


80 


32 


80 


8 


9 4 


32 


76 


9 


09 


32 


72 


9 


23 


34 


35 


33 


81 


9 


06 


33 


77 


9 


21 


33 


73 


9 


35 


33 


69 


9 


• 5o 


35 


36 


34 


77" 


9 


32 


34 


73 


9 


47 


34 


tl 


9 


62 


34 


65 


9 


•77 


36 


3 7 


35 


74 


9 


58 


35 


70 


9 


73 


35 


9 


89 


35 


61 


10 


04 


ll 


38 


36 


71 


9 


84 


36 


66 


10 


00 


36 


62 


10 


16 


36 


57 


10 


•3i 


3 9 


37 


67 


10 


09 


37 


63 


10 


26 


37 


58 


10 


42 


37 


54 


10 


5 9 


3 9 


4o 


38 


64 


10 


3o 


38 


5 9 


10 


52 


38 


55 


10 


69 


38 


5o 


10 


86 


40 


4i 


3 9 


60 


10 


61 


39 


56 


10 


78 


3 9 


5i 


10 


96 


3 9 


46 


11 


i3 


4i 


42 


4o 


57 


10 


87 


4o 


52 


11 


o5 


4o 


47 


11 


22 


40 


42 


11 


40 


42 


43 


41 


53 


11 


i3 


41 


49 


11 


3i 


41 


44 


11 


49 


41 


39 


11 


67 


43 


44 


42 


5o 


11 


3 9 


42 


45 


11 


57 


42 


4o 


11 


76 


42 


35 


11 


94 


44 


45 


43 


47 


11 


6o 


43 


42 


11 


84 


43 


36 


12 


o3 


43 


3i 


12 


21 


45 


46 


44 


43 


11 


9 1 


44 


38 


12 


10 


44 


33 


12 


29 


44 


27 


12 


49 


46 


47 


45 


40 


12 


16 


45 


35 


12 


36 


45 


29 


12 


56 


45 


24 


12 


76 


47 


48 


46 


36 


12 


42 


46 


3i 


12 


63 


46 


25 


12 


83 


46 


20 


i3 


o3 


48 


4 9 


47 


• 33 


12 


• 68 


47 


27 


12 


89 


47 


22 


i3 


09 


47 


16 


i3 


3o 


49 


5o 


48 .3o 


12-94 


48-24 


i3-i5 


48-18 


i3-36 


48-12 


13.57 


5o 


£ 
a 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


CO 

a 


-*■» 
CO 

S 


















a 

as 

00 


7 


5° 


74£° 


^° 


74 


i° 

















Table IV. 




TRAVERSE TABLE. 




117 


B 

3 

a 


15° 


15i° 




151° 


15|° 




5" 

s 

? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


49-26 


l3-20 


49-20 


i3-4i 


49-i5 


13-63 


49-09 


i3-84 


5i 


52 


5o 


23 


i3 


46 


5o 


17 


13 


68 


5o 


II 


i3 


90 


5o 


o5 


14 


II 


52 


53 


5i 


l 9 


i3 


72 


5i 


i3 


i3 


94 


5i 


07 


14 


16 


5i 


01 


14 


39 


53 


54 


52 


16 


i3 


98 


52 


10 


14 


20 


52 


04 


14 


43 


5i 


97 


14 


66 


54 


55 


53 


i3 


14 


24 


53 


06 


14 


47 


53 


00 


14 


70 


52 


94 


14 


93 


55 


56 


54 


09 


U 


49 


54 


o3 


14 


73 


53 


96 


14 


97 


53 


90 


i5 


20 


56 


57 


55 


06 


14 


7 3 


54 


99 


14 


99 


54 


o3 


i5 


23 


54 


86 


i5 


47 


5 7 


58 


56 


02 


i5 


01 


55 


96 


i5 


26 


55 


k 


i5 


5o 


55 


82 


i5 


74 


58 


5 9 


56 


99 


i5 


27 


56 


92 


i5 


52 


56 


i5 


77 


56 


78 


16 


01 


5 9 


6o 


5 7 


96 


i5 


53 


57 


«9 


i5 


78 


57 


82 


16 


o3 


57 


75 


16 


29 


60 


6i 


58 


92 


i5 


79 


58 


85 


16 


04 


58 


78 


16 


3o 


58 


7 1 


16 


56 


61 


62 


5 9 


89 


16 


o5 


5 9 


82 


16 


3i 


5 9 


75. 


16 


57 


5 9 


67 


16 


83 


62 


63 


6o- 


85 


16 


3i 


60 


78 


16 


57 


60 


7 1 


16 


84 


60 


63 


*7 


10 


63 


64 


61 


82 


16 


56 


61 


7 5 


16 


83 


61 


67 


*7 


10 


61 


60 


n 


37 


64 


65 


62. 


79 


16 


82 


62 


71 


«7 


10 


62 


64 


17 


37 


62 


56 


17 


64 


65 


66 


63- 


73 


17 


08 


63 


68 


17 


36 


63 


60 


n 


64 


63 


52 


17 


92 


66 


67 


64 


72 


n 


34 


64 


64 


n 


62 


64 


56 


17 


90 


64 


48 


18 


J 9 


67 


68 


65< 


68 


n 


60 


65 


61 


n 


80 


65 


53 


18 


17 


65 


45 


18 


46 


68 


69 


66- 


65 


n 


86 


66 


57 


18 


i5 


66 


49 


18 


44 


66 


4i 


18 


73 


69 


70 


67 


61 


18 


12 


67 


54 


18 


4i 


6 T 


45 


18 


71 


67 


37 


19 


00 


70 


7i 


68 


58 


18 


38 


68 


5o 


18 


68 


68 


42 


18 


97 


68 


33 


l 9 


27 


71 


72 


69 


55 


18 


63 


69 


46 


18 


94 


69 


38 


19 


24 


69 


3o 


l 9 


54 


72 


73 


70 


5i 


18 


89 


70 


43 


J 9 


20 


70 


35 


J 9 


5i 


70 


26 


19 


82 


73 


74 


71 


48 


*g 


i5 


7i 


3 9 


1 9 


46 


7 1 


3i 


*9 


78' 


7i 


22 


20 


09 


74 


7 5 


72 


44 


l 9 


4i 


72 


36 


l 9 


73 


7.2 


27 


20 


04 


72 


18 


20 


36 


75 


76 


73 


41 


*9 


67 


73 


32 


19 


99 


73 


24 


20 


3i 


73 


i5 


20 


63 


76 


9 


74- 


38 


l 9 


93 


74 


29 


20 


25 


74 


20 


20 


58 


74 


11 


20 


90 


77 


75- 


34 


20 


19 


75 


.25 


20 


52 


75 


16 


20 


84 


75 


07 


21 


17 


78 


29 


76. 


3i 


20 


45 


76. 


22 


20 


78 


76 


i3 


21 


11 


76 


o3 


21 


44 


I 9 


80 


77- 


27 


20 


7i 


77 


18 


21 


04 


77 


09 


21 


38 


77 


00 


21 


72 


80 


81 


78 


24 


20 


96 


73 


i5 


21 


3i 


78 


o5 


21 


65 


77 


96 


21 


99 


81 


82 


79 


21 


21 


22 


79 


11 


21 


57 


79 


02 


21 


9 1 


78 


92 


22 


26 


82 


83 


80 


17 


21 


48 


80 


08 


21 


83 


79 


98 


22 


18 


79 


88 


22 


53 


83 


84 


81 


14 


21 


74 


81 


04 


22 


09 


80 


94 


22 


45 


80 


85 


22 


80 


84 


85 


82 


10 


22 


00 


82 


01 


22 


36 


81 


91 


22 


72 


81 


81 


23 


07 


85 


86 


83 


07 


22 


26 


82 


97 


22 


62 


82 


87 


22 


98 


82 


77 


23 


34 


86 


87 


84 


04 


22 


52 


83 


94 


22 


88 


83 


84 


23 


25 


83 


73 


23 


62 


87 


88 


85 


00 


22 


78 


84 


90 


23 


i5 


84 


80 


23 


52 


84 


70 


23 


89 


88 


89 


85 


97 


23 


o3 


85 


87 


23 


41 


85 


76 


23 


78 


85 


66 


24 


16 


89 


90 


86 


9 3 


23 


29 


86 


83 


23 


67 


86 


73 


24 


o5 


86 


62 


24 


43 


90 


9i 


87 


90 


23 


55 


87 


80 


23 


94 


87 


69 


24 


32 


87 


58 


24 


70 


91 


92 


88 


87 


23 


81 


88 


76 


24 


20 


88 


65 


24 


59 


88 


55 


24 


97 


92 


9 3 


89 


83 


24 


07 


89 


73 


24 


46 


89 


62 


24 


85 


89 


5i 


25 


24 


93 


9 i 


90 


80 


24 


33 


90 


69 


24 


72 


90 


58 


25 


12 


90 


47 


25 


52 


94 


9 5 


9 1 


.76 


24 


5 9 


9 1 


65 


24 


99 


9 1 


54 


25 


3 9 


9 1 


43 


25 


79 


9? 


96 


92 


73 


24 


85 


92 


62 


25 


25 


92 


5i 


25 


65 


92 


40 


26 


06 


96 


97 


93 


69 


25 


11 


93 


58 


25 


5i 


93 


47 


25 


92 


93 


36 


26 


33 


9 l 


98 


94 


66 


25 


36 


94 


55 


25 


78 


94 


44 


26 


*9 


94 


32 


26 


60 


98 


99 


9 5 


■63 


25 


• 62 


9 5 


5i 


26 


04 


9 5 


•40 


26 


46 


9 5 


28 


26 


87 


99 


100 


96-59 


25-88 


96-48 


26-3o 


96 -36 


26-75 


96-25 


27-14 


100 


6 


c 

m 

5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


$ 

a 

el 

a 


tf< 


)° 


*74|° 


w 


w 


i° 





118 






TRAVERSE TABLE. 




Table IV. 


a 

3 


16° 


16i° 


1«*° 


16 


30 


ST 

3 
a 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


0-96 


0-28 


0-96 


0-28 


0-96 


0-28 


0-96 


0-29 


I 


2 


I- 


92 


0- 


55 


1 


92 





56 


I- 


92 


0' 


5 7 


I 


92 





58 


2^ 


3 


2- 


88 


0- 


83 


2 


88 





84 


2 


88 





85 


2 


87 





86 


3 


4 


3 


85 


I- 


10 


3 


84 


I 


1.2 


3 


84 


I 


14 


3 


83 


1 


i5 


4 


5 


4- 


81 


I- 


38 


4 


80 


I 


4o 


4 


79 


I 


42 


4 


79 


1 


44 


5 


6 


5 


77 


I- 


65 


5 


76 


I 


68 


5 


75 


I 


70 


5 


7 5 


1 


73 


6 


7 


6 


73 


I- 


93 


6 


72 


I 


96 


* 6 


7i 


I 


99 


6 


70 


2 


02 


7 


8 


7 


69 


2 


21 


7 


68 


2 


24 


7 


67 


2 


27 


7 


66 


2 


3i 


8 


9 


8 


65 


2 


48 


8 


64 


2 


52 


8 


63 


2 


56 


8 


62 


2 


5 9 


9 


10 


9 


61 


2 


76 


9 


60 


2 


80 


9 


5 9 


2 


84 


9 


58 


2 


88 


10 


ii 


10 


57 


3 


o3 


10 


56 


3 


08 


10 


55 


3 


12 


10 


53 


3 


17 


11 


12 


11 


54 


3 


3i 


11 


52 


3 


36 


11 


5i 


3 


4i 


11 


49 


3 


46 


12 


i3 


12 


5o 


3 


58 


12 


48 


3 


64 


12 


46 


3 


69 


12 


45 


3 


75 


i3 


U 


i3 


46 


3 


86 


i3 


44 


3 


92 


i3 


42 


3 


98 


i3 


41 


4 


o3 


14 


i5 


14 


42 


4 


i3 


14 


4o 


4 


20 


14 


38 


4 


26 


14 


36 


4 


32 


i5 


i.6 


i5 


38 


, 4 


41 


i5 


36 


4 


48 


i5 


34 


4 


54 


i5 


32 


4 


61 


16 


17 


16 


34 


4 


69 


16 


32 


4 


76 


16 


3o 


4 


83 


16 


28 


4 


90 


17 


18 


17 


3o 


4 


96 


n 


28 


5 


04 


17 


26 


5 


11 


r 2 


24 


5 


19 


18 


*9 


18 


26 


5 


24 


18 


24 


5 


32 


18 


22 


5 


4o 


18 


• 19 


5 


48 


l 9 


20 


*9 


23 


5 


5i 


19 


20 


5 


60 


19 


18 


5 


68 


19 


•ID 


5 


76 


20 


21 


20 


*9 


5 


79 


20 


16 


5 


88 


20 


14 


5 


96 


20 


II 


6 


o5 


21 


22 


21 


i5 


6 


06 


21 


12 


6 


16 


21 


09 


6 


25 


21 


07 


6 


34 


22 


23 


22 


11 


6 


34 


22 


08 


6 


44 


22 


o5 


6 


• 53 


22 


•02 


6 


63 


23 


24 


23 


07 


6 


62 


23 


04 


6 


72 


23 


01 


6 


• 82 


22 


98 


6 


92 


24 


23 


24 


o3 


6 


89 


24 


00 


7 


00 


23 


97 


7 


• 10 


23 


• 9 4 


7 


20 


25 


26 


24 


9? 


7 


n 


24 


96 


7 


28 


24 


2 3 


7 


38 


24 


•90 


7 


4 2 


26 


27 


25 


95 


7 


44 


25 


92 


7 


56 


25 


89 


7 


67 


25 


• 85 


7 


78 


27 


28 


26 


92 


7 


72 


26 


88 


I 


84 


26 


85 


7 


9 5 


26 


81 


8 


07 


28 


29 


27 


88 


7 


99 


27 


84 


11 


27 


81 


8 


24 


27 


77 


8 


36 


29 


3o 


28 


84 


8 


27 


28 


80 


8 


39 


28 


76 


8 


52 


28 


73 


8 


65 


3o 


3i 


29 


80 


8 


54 


29 


76 


8 


67 


29 


72 


8 


80 


29 


68 


8 


93 


3i 


32 


3o 


76 


8 


82 


3o 


72 


8 


9 5 


3o 


68 


9 


09 


3o 


64 


9 


22 


32 


33 


3i 


72 


9 


10 


3i 


68 


9 


23 


3i 


64 


9 


37 


3i 


60 


9 


5i 


33 


34 


32 


68 


9 


37 


32 


64 


9 


5i 


32 


60 


9 


66 


32 


56 


9 


80 


34 


35 


33 


64 


9 


65 


33 


60 


9 


79 


33 


56 


9 


•94 


33 


5i 


10 


09 


35 


36 


34 


61 


9 


92 


34 


56 


10 


07 


34 


•52 


10 


• 22 


34 


•47 


10 


38 


36 


37 


35 


57 


10 


20 


35 


52 


10 


35 


35 


• 48 


10 


•5i 


35 


• 43 


10 


66 


37 


38 


36 


53 


10 


47 


36 


48 


10 


63 


36 


•44 


10 


•79 


36 


• 3 9 


10 


9 5 


38 


39 


37 


49 


10 


75 


37 


•44 


10 


9 1 


37 


•3 9 


11 


• 08 


37 


• 35 


11 


24 


39 


40 


38 


45 


11 


o3 


38 


40 


11 


19 


38 


• 35 


11 


• 36 


38 


•3o 


11 


53 


40 


4i 


3 9 


4i 


11 


3o 


39 


36 


11 


•47 


39 


•3i 


11 


• 64 


39 


.26 


11 


82 


4i 


42 


4o 


37 


11 


58 


40 


32 


11 


• 7 5 


4o 


• 27 


11 


• 9 3 


4o 


• 22 


12 


10 


42 


43 


4i 


33 


11 


85 


41 


.28 


12 


-o3 


41 


•23 


12 


• 21 


41 


• 18 


12 


3 9 


43 


44 


42 


3o 


12 


i3 


42 


•24 


12 


•3i 


42 


• 19 


12 


• 5o 


42 


•i3 


12 


68 


44 


45 


43 


• 26 


12 


40 


43 


• 20 


12 


-5 9 


43 


• i5 


12 


•78 


43 


•09 


12 


97 


45 


46 


44 


•22 


12 


68 


44 


.16 


12 


.87 


44 


•11 


i3 


• 06 


44 


•o5 


i3 


26 


46 


47 


45 


.18 


12 


9 5 


45 


■ 12 


i3 


-i5 


45 


• 06 


i3 


•35 


45 


01 


i3 


55 


47 


48 


46 


•14 


i3 


•23 


46 


.08 


i3 


■43 


46 


•02 


i3 


• 63 


45 


•96 


i3 


83 


48 


i 9 


47 


• 10 


i3 


•5i 


47 


.04 


i3 


•7i 


46 


.98 


i3 


•92 


46 


92 


14 


12 


49 


5o 


48-06 


13.78 


48-00 


i3-99 


47-94 


14-20 


47-88 


i4-4i 


5o 





Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 





















c 

M 


CQ 

5 


7 

1 


4° 


73 


1° 


1Sh° 


73 


i° 


01 

5 



Table IV. 


TRAVERSE TABLE. 




119 


? 


16° 


16i° 


16i° 


16|° 


U 

3 

a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


49-02 


14-06 


48.96 


14-27 


48-90 


14-48 


48-84 


~ 14-70 


5i 


52 


49-99 


14-33 


49- 


92 


14- 


55 


49 


86 


14- 


77 


4 9 - 


79 


14- 


99 


52 


53 


3o -g5 


14-61 


5o 


88 


14- 


83 


5o 


82 


i5- 


o5 


5o- 


75 


i5 


27 


53 


54 


5I-QI 


14-88 


5i. 


84 


i5 


11 


5i 


78 


i5 


34 


5i. 


71 


i5 


56 


54 


55 


52-87 


i5-i6 


52- 


80 


i5 


39 


52 


74 


i5- 


62 


52- 


67 


i5 


85 


55 


56 


53-83 


i5-44 


53- 


76 


i5 


67 


53 


69 


i5 


90 


53- 


62 


16 


14 


56 


5 7 


54-79 


i5. 7 i 


54 


72 


i5 


9 5 


54 


65 


16. 


J 9 


54- 


58 


16 


43 


5 7 


58 


55.75 


15.99 


55- 


68 


16 


23 


55 


61 


16 


47 


55 


54 


16 


72 


58 


5 9 


56- 7 i 


16.26 


56- 


64 


16- 


5i 


56- 


57 


16 


76 


56- 


5o 


17 


00 


5 9 


6o 


5 7 - 68 


16.54 


5 7 . 


60 


16 


79 


57 


53 


17- 


04 


57 


45 


17 


29 


60 


6i 


58-64 


i6- 81 


58- 


56 


17' 


07 


58- 


49 


17' 


32 


58 


4i 


H 


58 


61 


62 


59-60 


17-09 


5 9 . 


52 


17- 


35 


5 9 


45 


17 


61 


5 9 


37 


H 


87 


62 


63 


60 -56 


17-37 


60. 


48 


17 


63 


60 


4i 


n 


89 


60 


33 


18 


16 


63 


64 


6i-52 


17-64 


61 • 


44 


'7 


9 1 


61 


36 


18 


18 


61 


28 


18 


44 


64 


65 


62-48 


17-92 


62 


40 


18 


l 9 


62 


32 


18 


46 


62 


24 


18 


73 


65 


66 


63-44 


18-19 


63- 


36 


18 


47 


63 


28 


18 


74 


63 


20 


J 9 


02 


66 


67 


64-40 


18-47 


64- 


32 


18 


75 


64 


24 


r 9 


o3 


64 


16 


J 9 


3i 


67 


68 


65-37 


18.74 


65 


28 


*9 


o3 


65 


20 


*9 


3i 


65 


11 


*9 


60 


68 


69 


66-33 


19-02 


66 


24 


l 9 


3i 


66 


16 


*9 


60 


66 


07 


*9 


89 


69 


70 


67-29 


19.29 


67 


20 


19 


5 9 


67 


12 


*9 


88 


67 


o3 


20 


17 


70 


7i 


68-25 


19-57 


68 


16 


19 


87 


68 


08 


20 


H 


67 


99 


20 


46 


7i 


72 


69-21 


i 9 -85 


69 


12 


20 


i5 


69 


o3 


20 


45 


68 


9 5 


20 


73 


72 


73 


70-17 


20-12 


70 


08 


20 


43 


69 


99 


20 


73 


69 


90 


21 


04 


73 


74 


71 • i3 


20-40 


7i 


04 


20 


7i 


70 


9 5 


21 


02 


70 


86 


21 


33 


74 


7 5 


72-09 


20-67 


72 


00 


20 


99 


7i 


01 


21 


3o 


7i 


82 


21 


61 


75 


76 


73-o6 


20-95 


72 


96 


21 


27 


72 


87 


21 


5 9 


72 


78 


21 


90 


76 


77 


74-02 


21-22 


73 


92 


21 


55 


73 


83 


21 


87 


73 


73 


22 


19 


77 


78 


74-98 


21 -5o 


74 


88 


21 


83 


74 


79 


22 


i5 


74 


6 2 


22 


48 


78 


79 


75.94 


21-78 


75 


84 


22 


11 


75 


75 


22 


44 


7 5 


65 


22 


77 


79 


80 


76-90 


22-05 


76 


80 


22 


3 9 


76 


7i 


22 


72 


76 


61 


23 


06 


80 


81 


77.86 


22-33 


77 


76 


22 


67 


77 


66 


23 


01 


77 


56 


23 


34 


81 


82 


78-82 


22-60 


78 


72 


22 


9 5 


78 


62 


23 


29 


78 


52 


23 


63 


82 


83 


79.78 


22-88 


79 


68 


23 


23 


79 


58 


23 


5 7 


79 


48 


23 


•92 


83 


84 


80.75 


23-i5 


80 


64 


23 


5i 


80 


54 


23 


86 


80 


44 


24 


21 


84 


85 


81-71 


23-43 


81 


60 


23 


79 


81 


5o 


24 


14 


81 


39 


24 


■5o 


85 


86 


82-67 


23-70 


82 


56 


24 


07 


82 


46 


24 


43 


82 


35 


24 


.78 


86 


87 


83-63 


23.98 


83 


52 


24 


35 


83 


42 


24 


7 1 


83 


3i 


25 


• 07 


8 1 


88 


84- 5 9 


24-26 


84 


48 


24 


62 


84 


38 


24 


99 


84 


27 


25 


■ 36 


88 


89 


85-55 


24-53 


85 


44 


24 


90 


'85 


33 


25 


28 


85 


22 


25 


•65 


89 


90 


86 -5i 


24-81 


86 


4o 


25 


18 


86 


•29 


25 


56 


86 


18 


25 


• 9 4 


90 


9 1 


87.47 


25-o8 


87 


36 


25 


46 


87 


•25 


25 


• 85 


87 


•14 


26 


-23 


91 


92 


88-44 


25-36 


88 


32 


25 


74 


88 


■ 21 


26 


■ i3 


88 


• 10 


26 


• 5i 


92 


9 3 


89-40 


25-63 


89 


28 


26 


02 


89 


•H 


26 


•4i 


89 


• o5 


26 


■ 80 


93 


94 


90-36 


25-91 


90 


24 


26 


3o 


90 


■ i3 


26 


70 


90 


• 01 


27 


-09 


9 i 


9 5 


91.32 


26-19 


9 1 


■20 


26 


58 


9 1 


• OQ 


26 


.98 


90 


•97 


27 


• 38 


95 


96 


92-28 


26-46 


92 


•l6 


26 


86 


92 


•03 


27 


■27 


9i 


• 9 3 


27 


.67 


96 


97 


93-24 


26.74 


93 


■12 


27 


•14 


9 3 


•01 


27 


■ 55 


92 


■88 


27 


• 9 5 


9 l 


98 


94-20 


27-01 


94 


•08 


27 


•42 


9 3 


.96 


27 


■ 83 


93 


•84 


28 


•24 


98 


99 


95-16 


27-29 


9 5 


■04 


27 


•70 


9 4 


.92 


28 


•12 


94 


• 8o 


28 


• 53 


99 


100 


96-13 


27-56 


96-00 


27.98 


9 5- 88 


28-40 


95.76 


28-82 


100 


6 
a 
Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


4) 
O 
S 
id 

a 


740 


73f° 


73i° 


m° 



120 




















LE. 










E IV. 








TRAVERSE TAE 




TABL! 




d 

M 

P 
3 
C5 

3 


17° 


174° 


I7i° 


17|° 


gj 

55* 

s 
a 
? 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




I 


0-96 


0-29 


0-95 


o-3o 


0-95 


o-3o 


0-95 


o-3o 


I 




2 


I 


oi 





58 


I 


91 





5 9 


I 


9 1 


o-6o 


I 


90 





61 


2 




3 


2 


87 





88 


2 


87 





89 


2 


86 


0-90 


2 


86 





9 1 


3 




4 


3 


83 


1 


17 


3 


82 


1 


19 


3 


8i 


1-20 


3 


81 


I 


22 


4 




5 


4 


78 


1 


46 


4 


78 


1 


48 


4 


77 


i-5o 


4 


76 


I 


52 


5 




6 


5 


74 


I 


75 


5 


73 


1 


78 


5 


72 


i- 80 


5 


7i 


I 


83 


6 




7 


6 


60 


2 


o5 


6 


69 


2 


08 


6 


68 


2-10 


6 


67 


2 


i3 


I 




8 


n 


65 


2 


34 


7 


64 


2 


37 


I 


63 


2-41 


7 


62 


2 


44 




9 


8 


61 


2 


63 


8 


60 


2 


67 


58 


2-71 


8 


57 


2 


•74 


9 




10 


9 


56 


2 


92 


9 


55 


2 


97 


9 


54 


3-oi 


9 


52 


3 


■o5 


10 




ii 


10 


52 


3 


22 


10 


5i 


3 


26 


10 


49 


3-3i 


10 


48 


3 


35 


11 




12 


11 


48 


3 


5i 


11 


46 


a 


56 


11 


44 


3-6i 


n 


43 


3 


66 


12 




i3 


12 


43 


3 


80 


12 


42 


3. 


85 


12 


40 


3.91 


12 


38 


3 


96 


1 3 




14 


i3 


3 9 


4 


09 


i3 


37 


4 


i5 


i3 


35 


4-ai 


i3 


33 


4 


27 


14 




i5 


14 


34 


4 


3 9 


14 


33 


4 


45 


14 


3i 


4-5i 


14 


29 


4 


57 


i5 




16 


i5 


3o 


4 


68 


i5 


28 


4 


74 


i5 


26 


4-81 


i5 


24 


4 


88 


16 




a 


16 


26 


4 


97 


16 


24 


5 


04 


16 


21 


5- 11 


16 


•19 


5 


.18 


17 




17 


21 


5 


26 


17 


19 


5 


34 


n 


n 


5-41 


\l 


14 


5 


.49 


18 




19 


18 


n 


5 


56 


18 


i5 


5 


63 


18 


12 


5.71 


•10 


5 


•79 


19 




20 


19 


i3 


5 


85 


19 


10 


5 


9 3 


*9 


07 


6-oi 


19 


•o5 


6 


■10 


20 




21 


20 


08 


6 


14 


20 


06 


6 


23 


20 


o3 


6-3i 


20 


00 


6 


•40 


21 




22 


21 


04 


6 


43 


21 


01 


6 


52 


20 


98 


6-62 


20 


9 5 


6 


•7i 


22 




23 


21 


99 


6 


72 


21 


97 


6 


82 


21 


2 4 


6-92 


21 


■91 


7 


■01 


23 




24 


22 


93 


7 


02 


22 


92 


7 


12 


22 


89 


7-22 


22 


86 


7 


•32 


24 




25 


23 


91 


7 


3i 


23 


88 


7 


41 


23 


84 


7-52 


23 


•81 


7 


■62 


25 




26 


24 


86 


7 


60 


24 


83 


7 


7i 


24 


80 


7-82 


24 


.76 




- 9 3 


26 




27 


25 


82 


7 


89 


25 


79 


8 


01 


25 


75 


8-12 


25 


7i 


8 


23 


27 




28 


26 


78 


8 


19 


26 


74 


8 


3o 


26 


70 


8-42 


26 


67 


8 


54 


28 




29 


27 


73 


8 


48 


27 


70 


8 


60 


27 


66 


8-72 


27 


62 


8 


84 


29 




3o 


28 


69 


8 


77 


28 


65 


8 


90 


28 


61 


9-02 


28 


57 


9 


i5 


3o 




3i 


29 


65 


9 


06 


29 


61 


9 


19 


29 


57 


9-32 


29 


52 


9 


45 


3i 




32 


3o 


60 


9 


36 


3o 


56 


9 


49 


3o 


52 


9-62 


3o 


48 


9 


76 


32 




33 


3i 


56 


9 


65 


3i 


52 


9 


79 


3i 


47 


9-92 


3i 


43 


10 


06 


33 




34 


32 


5i 


9 


94 


32 


47 


10 


08 


32 


43 


10-22 


32 


38 


10 


37 


34 




35 


33 


47 


10 


23 


33 


43 


10 


38 


33 


38 


10-52 


33 


33 


10 


67 


35 




36 


34 


43 


10 


53 


34 


38 


10 


68 


34 


33 


10-83 


34 


29 


10 


98 


36 




37 


35 


38 


10 


82 


35 


34 


10 


97 


35 


29 


ii-i3 


35 


24 


11 


28 


37 




38 


36 


34 


11 


11 


36 


29 


11 


27 


36 


24 


n-43 


36 


J 9 


11 


58 


38 




3 9 


37 


3o 


11 


40 


37 


25 


11 


57 


37 


19 


ii- 7 3 


37 


14 


11 


89 


39 




40 


38 


23 


11 


69 


38 


20 


11 


86 


38 


ID 


12-03 


38 


10 


12 


l 9 


4o 




4i 


3 9 


21 


11 


99 


3 9 


16 


12 


16 


3 9 


10 


12-33 


3 9 


o5 


12 


5o 


4i 




42 


40 


16 


12 


28 


40 


11 


12 


45 


4o 


06 


12-63 


4o 


00 


12 


80 


42 




43 


41 


12 


12 


5 7 


4i 


07 


12 


7 5 


4i 


01 


12-93 


4o 


9 5 


i3 


11 


43 




44 


42 


08 


12 


86 


42 


02 


i3 


o5 


4i 


96 


13-23 


4i 


H 


i3 


4i 


44 




45 


43 


o3 


i3 


16 


42 


98 


i3 


34 


42 


92 


13-53 


42 


i3 


72 


45 




46 


43 


99 


i3 


45 


43 


2 3 


i3 


64 


43 


87 


13-83 


43 


81 


14 


02 


46 




47 


44 


9 5 


i3 


74 


44 


89 


i3 


94 


44 


82 


i4-i3 


44 


76 


14 


33 


47 




48 


45 


90 


14 


o3 


45 


84 


14 


23 


45 


78 


U-43 


45 


7i 


14 


63 


48 




49 


46 


86 


14 


33 


46 


80 


14 


53 


46 


73 


14-73 


46- 


67 


14- 


94 


49 




5o 


47-82 


14-62 


47-75 


14-83 


47-69 


i5-o4 


47-62 


i5-24 


5o 





d 

M 

5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




1 




7 


3° 


72 


JO 


72 


h° 


72 


P 


1 





Table IV. 


TRAVERSE TABLE. 






121 


g 

1 

3 
a 
9 


17° 


m° 


m° 


17f° 


m 

s 

a 


Lat. Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


48-77 


vi4-9i 


48.71 


15-12 


48-64 


15-34 


48- 5 7 


i5-55 


5i 


52 


49-73 


l5-20 


49- 


66 


l5 


42 


49 


§9 


i5- 


64 


49- 


52 


i5 


85 


52 


53 


5o-68 


i5-5o 


5o- 


62 


i5 


72 


5o 


5o 


i5- 


94 


5o- 


48 


16 


16 


53 


54 


5i-64 


15.79 


5i- 


5 7 


16 


01 


5i 


5o 


16. 


24 


5i- 


43 


16 


46 


54 


55 


52-6o 


16-08 


52- 


53 


16 


3i 


52 


45 


16 


54 


52- 


38 


16 


77 


55 


56 


53-55 


16.37 


53- 


48 


16 


61 


53 


41 


16 


84 


53- 


33 


n 


07 


56 


5? 


54-5i 


16-67 


54- 


44 


16 


90 


54 


36 


n 


14 


54- 


29 


17 


38 


5 7 


58 


55.47 


16-96 


55- 


3 9 


17 


20 


55 


32 


n 


44 


55 


24 


n 


68 


58 


5 9 


56-42 


17-25 


56- 


35 


n 


5o 


56 


27 


17 


74 


56- 


19 


n 


99 


39 


6o 


57-38 


17.54 


5 7 . 


3o 


n 


79 


57 


22 


18 


04 


57 


U 


18 


29 


60 


6i 


58-33 


17-83 


58- 


26 


18 


09 


58 


18 


18 


34 


58 


10 


18- 


60 


6l 


62 


59-29 


18. i3 


5 9 - 


21 


18 


39 


5 9 


i3 


18 


64 


5 9 


o5 


18 


90 


62 


63 


6o-25 


18-42 


60 • 


n 


18 


68 


60 


08 


18 


94 


60 


00 


*9 


21 


63 


64 


6l -20 


18.71 


61 « 


12 


18 


98 


61 


04 


*9 


25 


60 


9 5 


J 9 


5i 


64 


65 


62-16 


19-00 


62- 


08 


»9 


28 


61 


99 


J 9 


55 


61 


9 1 


J 9 


82 


65 


66 


63-12 


19.30 


63- 


o3 


x 9 


5 7 


62 


95 


1 9 


85 


62- 


86 


20 


12 


66 


67 


64-07 


i9-5 9 


63 


99 


19 


87 


63 


90 


20 


i5 


63 


81 


20 


43 


67 


68 


65- o3 


19-88 


64 


94 


20 


16 


64 


85 


20 


45 


64 


76 


20 


73 


68 


69 


65 -99 


20-17 


65 


90 


20 


46 


65 


81 


20 


73 


65 


72 


21 


04 


69 


70 


66-94 


20-47 


66- 


85 


20 


76 


66 


76 


21 


o5 


66 


67 


21 


34 


70 


71 


67-90 


20-76 


67 


81 


21 


o5 


67 


7i 


21 


35 


67 


62 


21 


65 


71 


72 


68-85 


21 -o5 


68 


76 


21 


35 


68 


67 


21 


65 


68 


5 7 


21 


9 5 


72 


73 


69-81 


21-34 


69 


72 


21 


65 


69 


62 


21 


9 5 


69 


52 


22 


26 


73 


74 


70-77 


21-64 


70 


67 


21 


94 


70 


58 


22 


25 


70 


48 


22 


56 


74 


7 5 


71-72 


21-93 


7i 


63 


22 


24 


7i 


53 


22 


55 


7i 


43 


22 


86 


75 


76 


72-68 


22-22 


72 


58 


22 


54 


72 


48 


22 


85 


72 


38 


23 


n 


76 


8 


73-64 


22-5l 


73 


54 


22 


83 


73 


44 


23 


i5 


73 


33 


23 


47 


u 


74-59 


22-80 


74 


4q 


23 


i3 


74 


39 


23 


46 


74 


29 


23 


78 


78 


79 


75-5D 


23-10 


75 


45 


23 


43 


75 


34 


23 


76 


75 


24 


24 


08 


79 


80 


76 -5o 


23-39 


76 


4o 


23 


72 


76 


3o 


24 


06 


76 


19 


24 


39 


80 


81 


77.46 


23-68 


77 


36 


24 


02 


77 


25 


24 


36 


77 


14 


24 


.69 


81 


82 


78-42 


23-97 


78 


3i 


24 


32 


78 


20 


24 


66 


78 


10 


25 


00 


82 


83 


79-37 


24-27 


79 


27 


24 


61 


79 


16 


25 


96 


79 


o5 


25 


3o 


83 


84 


8o-33 


24-56 


80 


22 


24 


9 1 


80 


11 


25 


26 


80 


00 


25 


61 


84 


85 


81-29 


24-85 


81 


18 


25 


21 


81 


07 


25 


■ 56 


80 


• 9 5 


25 


■ 91 


85 


86 


82-24 


25-14 


82 


i3 


25 


5o 


82 


02 


25 


• 86 


81 


• 91 


26 


• 22 


86 


87 


83-20 


25-44 


83 


09 


25 


•80 


82 


•97 


26 


• 16 


82 


■ 86 


26 


•52 


87 


88 


84- 15 


25-73 


84 


04 


26 


•10 


83 


- 9 3 


26 


• 46 


83 


• 8i 


26 


•83 


88 


89 


85-n 


26-02 


85 


00 


26 


•3 9 


84 


• 88 


26 


.76 


84 


.76 


27 


• i3 


89 


90 


86-07 


26-3i 


85 


9 5 


26 


.69 


85 


■ 83 


27.06 


85 


.72 


27 


•44 


90 


91 


87-02 


26-61 


86 


91 


26 


•99 


86 


•79 


27.36 


86 


.67 


27 


•74 


9* 


92 


87-98 


26-90 


87 


86 


27 


•28 


87 


•74 


27.66 


87 


.62 


28 


• o5 


92 


9 3 


88- 9 4 


27-19 


88 


82 


27 


• 58 


88 


.70 


27.97 


88 


57 


28 


• 35 


93 


9* 


89-89 


27-40 


89 


77 


27 


■87 


89 


• 65 


28-27 


89 


• 53 


28 


• 66 


9i 


9 5 


90-85 


27.78 


90 


■73 


28 


•n 


90 


■ 60 


28-57 


90 


48 


28 


.96 


9 5 


96 


91-81 


28-07 


9 1 


68 


28 


•47 


9 1 


• 56 


28-87 


9 1 


43 


29 


•27 


96 


91 


92-76 


28-36 


92 


• 64 


28 


.76 


92 


•5i 


29-17 


92 


38 


29 


5 7 


92 


98 


93-72 


28-65 


93 


• 5 9 


29 


•06 


93 


• 46 


29-47 


93 


33 


29 


• 88 


98 


99 


94-67 


28-94 


94 


■ 55 


29 


•36 


94 


■42 


29-77 


94 


29 


3o 


18 


99 


100 


9 5-63 


29-24 


95-5o 


29.65 


90-37 


30-07 


90-24 


3o-49 


100 


6 

a 
3 

3 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


oi 


a 

si 

Q 


1Z° 


72|° 


72£° 


72 


*° 



122 






TRAVERSE TABLE. 




Table IV. 


5 

ft- 
a 

CD 


18 


1° 


184° 


18i° 


18 


1° 


g 

s 
a 
CD 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


0-95 


o-3i 


0-95 


o-3i 


0-95 


0-32 


0- 9 5 


0-32 


I 


2 


1-90 


0- 


62 


I • 


90 


0- 


63 


I- 


90 


0- 


63 


I- 


89 





64 


2 


3 


2-85 


0- 


93 


2- 


85 





94 


2- 


84 


0- 


9 5 


2 


84 





96 


3 


4 


3-8o 


i- 


24 


3- 


80 


I- 


25 


3 


79 


I 


27 


3 


71 


I 


29 


4 


5 


4.76 


i- 


55 


4- 


75 


i- 


5 7 


4 


74 


I- 


5 9 


4 


1 


61 


5 


6 


5-71 


I- 


85 


5 


70 


I- 


88 


5 


69 


I 


90 


5 


68 


I 


93 


6 


J 


6-66 


2- 


16 


6 


65 


2- 


*9 


6 


64 


2 


22 


6 


63 


2 


25 


2 


7-61 


2- 


47 


7 


60 


2 


5i 


7 


5 9 


2 


54 


I 


58 


2 


5 7 


9 


8-56 


2- 


78 


8 


55 


2 


82 


8 


53 


2 


86 


52 


2 


89 


9 


10 


9-5i 


3 


09 


9 


5o 


3 


i3 


9 


48 


3 


n 


9 


47 


3 


21 


10 


ii 


10-46 


3- 


4o 


10 


45 


3 


44 


10 


43 


3 


49 


10 


42 


3 


54 


11 


12 


11 -4i 


3 


71 


11 


40 


3 


76 


11 


38 


3 


81 


11 


36 


3 


86 


12 


i3 


12-36 


4 


02 


12 


35 


4 


07 


12 


33 


4 


12 


12 


3i 


4 


18 


i3 


14 


i3-3i 


4 


33 


i3 


3o 


4 


38 


i3 


28 


4 


44 


i3 


26 


4 


5o 


14 


i5 


14-27 


4- 


64 


14 


25 


4 


70 


14 


22 


4 


76 


14 


20 


4 


82 


i5 


16 


l5-22 


4- 


94 


i5 


20 


5 


01 


i5 


17 


5 


08 


i5 


i5 


5 


14 


16 


17 


16-17 


5 


25 


16 


14 


5 


32 


16 


12 


5 


39 


16 


10 


5 


46 


•3 


i8 


17-12 


5 


56 


\l 


09 


5 


64 


17 


07 


5 


7i 


17 


04 


5 


79 


i9 


18-07 


5 


87 


04 


5 


9 5 


18 


02 


6 


o3 


n 


■99 


6 


11 


*9 


20 


I9-02 


6 


18 


18 


99 


6 


26 


18 


97 


6 


35 


18 


• 9 4 


6 


43 


20 


21 


I9.97 


6 


49 


19 


Q4 


6 


58 


19 


91 


6 


66 


19 


:8 


6 


75 


21 


22 


20-O2 


6 


80 


20 


89 


6 


89 


20 


86 


6 


98 


20 


7 


07 


22 


23 


21-87 


7 


11 


21 


84 


7 


20 


21 


81 


7 


Jo 


21 


.78 


7 


39 


23 


24 


22-83 


7 


42 


22 


79 


7 


52 


22 


76 


7 


62 


22 


•73 


7 


7 1 


24 


25 


23.78 


7 


73 


23 


74 


7 


83 


23 


7i 




93 


23 


.67 


8 


04 


25 


26 


24-73 


8 


o3 


24 


69 


8 


14 


24 


66 


8 


25 


24 


.62 


8 


36 


26 


a 


25-68 


8 


34 


25 


64 


8 


46 


25 


60 


8 


.57 


25 


•57 


8 


68 


27 


26-63 


8 


65 


26 


5 9 


8 


77 


26 


55 


8 


88 


26 


• 5i 


9 


00 


28 


29 


27-58 


8 


96 


27 


54 


9 


08 


27 


5o 


9 


20 


27 


•46 


9 


32 


29 


3o 


28-53 


9 


27 


28 


4 9 


9 


3 9 


28 


45 


9 


•52 


28 


4i 


9 


64 


3o 


3i 


29.48 


9 


58 


29 


44 


9 


7i 


29 


40 


9 


84 


29 


35 


9 


96 


3i 


32 


3o-43 


9 


89 


3o 


39 


10 


02 


3o 


35 


10 


i5 


3o 


• 3o 


10 


29 


32 


33 


3i-38 


10 


20 


3i 


34 


10 


33 


3i 


29 


10 


47 


3i 


•25 


10 


6i 


33 


34 


32-34 


10 


5i 


32 


29 


10 


65 


32 


24 


10 


79 


32 


20 


10 


93 


34 


35 


33-29 


10 


82 


33 


24 


10 


96 


33 


x 9 


11 


•11 


33 


•14 


11 


25 


35 


36 


34-24 


11 


12 


34 


l 9 


11 


27 


34 


■14 


11 


•42 


34 


• 09 


11 


07 


36 


37 


35-19 


11 


43 


35 


14 


11 


5 9 


35 


.09 


11 


.74 


35 


• 04 


11 


89 


37 


38 


36-14 


11 


74 


36 


09 


11 


90 


36 


■ 04 


12 


• 06 


35 


.98 


12 


21 


38 


3 9 


37-09 


12 


o5 


37 


04 


12 


21 


36 


.98 


12 


•37 


36 


• o3 


12 


54 


39 


4o 


38-o4 


12 


36 


37 


99 


12 


53 


37 


- 9 3 


12 


.69 


37 


• 88 


12 


86 


40 


4i 


38-99 


12 


67 


38 


,04 


12 


•84 


38 


• 88 


i3 


• 01 


38 


.82 


i3 


18 


4i 


42 


39-94 


12 


98 


3 9 


89 


i3 


• i5 


3 9 


-83 


i3 


• 33 


3 9 


•77 


i3 


5o 


42 


43 


40-90 


i3 


29 


40 


• 84 


i3 


■47 


40 


.78 


i3 


• 64 


4o 


.72 


i3 


82 


43 


44 


4i-85 


i3 


60 


41 


•79 


i3 


.78 


4i 


- 7 3 


i3 


.96 


41 


• 66 


14 


14 


44 


45 


42-80 


i3 


9 1 


42 


•74 


14 


• 09 


42 


.67 


14 


.28 


42 


• 61 


14 


46 


45 


46 


43-75 


14 


■21 


43 


.69 


14 


•4i 


43 


.62 


14 


.60 


43 


• 56 


14 


79 


46 


47 


44-70 


14 


•52 


44 


• 64 


14 


• 72 


44 


• 5 7 


14 


• 91 


44 


• 5i 


i5 


11 


47 


48 


45-65 


14 


•83 


45 


• 5 9 


i5 


• o3 


45 


•52 


i5 


•23 


45 


•45 


i5 


43 


48 


49 


46-60 


i5 


•14 


46 


•54 


i5 


■ 35 


46 


•47 


i5 


• 55 


46 


40 


i5 


7 5 


49 


5o 


47-55 


i5-45 


47-48 


15-66 


47-42 


15-87 


47-35 


16-07 


5o 





(3 
cfl 
w 

5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




a 
a 


7 


2° 


71 


r 


71i° 


71 


i° 


S 



Table IV. 


TRAVERSE TABLE. 




123 


3 


18° 


18i° 


18- 


\° 


18|° 


U 

s 
<B 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


48 -5o 


15.76 


48-43 


15-97 


48-36 


l6- 18 


48-29 


16-39 


5i 


52 


49-45 


16-07 


4 9 - 


38 


16- 


28 


49-3i 


l6- 


5o 


49-24 


l6- 


7 1 


52 i 


53 


5o-4i 


i6-38 


5o- 


33 


16- 


60 


5o-26 


l6- 


82 


50-19 


n- 


04 


53 


54 


5i-36 


16-69 


5i- 


28 


16- 


9 1 


5l-2I 


17- 


i3 


5i-i3 


i?" 


36 


54 


55 


52-3i 


17-00 


52- 


23 


17* 


22 


52-i6 


17- 


45 


52- 08 


n- 


68 


55 


56 


53-26 


i7-3o 


53- 


18 


17- 


54 


53- n 


17- 


77 


53 -o3 


i8- 


00 


56 


5 7 


54-21 


17-61 


54- 


i3 


17- 


85 


54 -o5 


l8- 


09 


53- 9 8 


18. 


32 


5 7 


58 


55.i6 


17-92 


55- 


08 


i8- 


16 


55-oo 


18. 


40 


54-92 


18- 


64 


58 


5 9 


56-11 


i8.23 


56- 


o3 


i8- 


48 


55-95 


18- 


72 


55-8 7 


18 


96 


5 9 


6o 


57-06 


18.54 


56- 


98 


i8- 


79 


56-90 


19. 


04 


56-82 


19 


29 


60 


6i 


58-01 


18. 85 


57- 


9 3 


19- 


10 


5 7 - 85 


19 


36 


57-76 


l 9 


61 


61 


62 


58.97 


19-16 


58- 


88 


19. 


42 


58- 80 


l 9 


67 


58- 7 i 


19 


93 


62 


63 


59-92 


19.47 


5 9 - 


83 


19- 


73 


59.74 


l 9 


99 


59-66 


20- 


25 


63 


64 


60-87 


19-78 


6o- 


78 


20 


04 


60-69 


20 


3i 


6o-6o 


20- 


57 


64 


65 


61-82 


20-09 


6i- 


73 


20 


36 


61-64 


20 


62 


6i-55 


20- 


89 


65 


66 


62-77 


20-40 


62- 


68 


20 


67 


62-59 


20 


94 


62 -5o 


21 


22 


66 


67 


63-72 


20-70 


63- 


63 


20 


98 


63-54 


21 


26 


63-44 


21 


54 


67 


68 


64-67 


21-01 


64- 


58 


21 


3o 


64-49 


21 


58 


64 -3 9 


21 


86 


68 


69 


65-62 


21-32 


65 


53 


21 


61 


65-43 


21 


89 


65-34 


22 


18 


69 


70 


66- 5 7 


21-63 


66 


48 


21 


92 


66-38 


22 


21 


66-29 


22 


5o 


70 


71 


67.53 


21-94 


67 


43 


22 


23 


67.33 


22 


53 


67-23 


22 


82 


7i 


72 


68-48 


22-25 


68 


38 


22 


55 


68-28 


22 


85 


68-18 


23 


14 


72 


73 


69-43 


22-56 


69 


33 


22 


86 


69-23 


23 


16 


69.13 


23 


47 


73 


74 


70-38 


22-87 


70 


28 


23 


n 


70-18 


23 


48 


70-07 


23 


79 


74 


75 


71-33 


23.18 


7i 


23 


23 


49 


71-12 


23 


80 


71-02 


24 


11 


75 


76 


72-28 


23-49 


72 


18 


23 


80 


72-07 


24 


12 


71-97 


24 


43 


76 


3 


73-23 


23-79 


73 


i3 


24 


11 


73-02 


24 


43 


72-91 


24 


75 


77 


74-i8 


24- 10 


74 


08 


24 


43 


73-97 


24 


7 5 


73-86 


25 


07 


78 


79 


70.i3 


24-41 


75 


o3 


24 


74 


74-92 


25 


07 


74-8i 


25 


3 9 


79 


80 


76-08 


24-72 


75 


98 


25 


o5 


75-87 


25 


38 


75.75 


25 


72 


80 


81 


77-04 


25-o3 


76 


93 


25 


37 


76-81 


23 


70 


76-70 


26 


04 


81 


82 


77-99 


25-34 


77 


88 


25 


68 


77.76 


26 


02 


77*65 


26 


36 


82 


83 


78-94 


25-65 


78 


83 


25 


99 


78-71 


26 


34 


78-60 


26 


68 


83 


84 


79-89 


25-96 


79 


77 


26 


3i 


79-66 


26 


65 


79-54 


27 


00 


84 


85 


80 -84 


26-27 


80 


72 


26 


62 


8o-6i 


26 


97 


80-49 


27 


32 


85 


86 


8i- 79 


26-58 


81 


67 


26 


93 


8i- 56 


27 


29 


8i-44 


27 


64 


86 


§3 


82-74 


26-88 


82 


62 


27 


25 


82 -5o 


27 


61 


82-38 


27 


97 


87 


83-6g 


27-19 


83 


• 5 7 


27 


56 


83-45 


27 


.92 


83-33 


28 


-29 


88 


89 


84-64 


27 -5o 


84 


•52 


27 


■87 


84-4o 


28 


•24 


84-28 


28 


•61 


89 


90 


85-6o 


27-81 


85 


•47 


28 


.18 


85-35 


28 


■ 56 


85-22 


28 


93 


90 


9 1 


86-55 


28-12 


86 


•42 


28 


• 5o 


86- 3o 


28 


•87 


86-17 


29 


•25 


9 1 


92 


87.50 


28-43 


87 


■37 


28 


• 81 


87-25 


29 


.19 


87-12 


29 


■57 


92 


9 3 


88-45 


28-74 


88 


•32 


29 


• 12 


88-19 


29 


• 5i 


88-o6 


29 


.89 


93 


94 


89-40 


29-05 


89 


.27 


29 


•44 


89-14 


29 


•83 


89-01 


3o 


• 22 


9 i 


9 5 


90-35 


29-36 


90 


•22 


29 


- 7 5 


90-09 


3o 


•14 


89.96 


3o 


-54 


9 5 


96 


91 -3o 


29-67 


9i 


•17 


3o 


-06 


91-04 


3o 


• 46 


90.91 


3o 


-86 


96 


97 


92-25 


29-97 


92 


•12 


3o 


-38 


91-99 


3o 


.78 


91-83 


3i 


• 18 


9 l 


98 


93-20 


3o-28 


93 


-07 


3o 


.69 


92-94 


3i 


• 10 


92-80 


3i 


-5o 


98 


99 


9 4-i5 


3o-59 


94 


•02 


3i 


• 00 


93-88 


3i 


•4i 


93.75 


3i 


-82 


99 


100 


95-11 


30-90 


94-97 


3i-32 


94-83 


3i-73 


94.69 


32-14 


100 




C 

EC 

(5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 


| 

i 


72° 


1 

7lf° 


m 


i° 


■7U° 

















124 



TRAVERSE TABLE. 



Table IV. 



19< 



Lat. 



Dep. 



9 

10 

ii 

12 

i3 
14 
i5 
16 

17 
18 

19 
20 

21 
22 

23 

24 

25 

26 

27 

28 

29 

3o 
3i 

32 

33 
34 
35 
36 

37 
38 
3 9 
4o 

4i 
42 
43 
44 
45 
46 

47 
48 

& 



10 
11 
12 

i3 

u 

i5 
16 

18 

*9 
20 
21 
22 

23 

24 

25 

26 
27 
28 

29 

3o 
3i 

32 

33 

34 
34 
35 
36 
37 

38 
3 9 ■ 
40 
41 
42 
43 
44 
45 
46 
47 



)5 

8? 

78 

73 
67 
62 
56 
5i 
.46 

40 
35 
29 

24 
18 
i3 

°7 
02 
96 
91 

86 

80 

75 
69 
64 
58 
53 

47 
42 

37 

3i 
26 
20 
i5 
09 
04 

98 
9 3 
88 
82 

77 
7i 
66 
60 
55 

49 
44 

38 
33 
28 



Dep. 



Lat. 



11° 



•33 


o- 


• 65 


I- 


.98 


2- 


• 3o 


3- 


• 63 


A- 


. 9 5 


5- 


■28 


6- 


• 6o 


7- 


• 9 3 


8- 


.26 


9' 


• 58 


10- 


•Qi 


ii- 


•23 


12- 


• 56 


i3- 


• 88 


i4- 


•21 


i5- 


• 53 


16. 


• 86 


16. 


.19 


IV 


•5i 


18. 


• 84 


19. 


• 16 


20- 


.49 


21- 


• 81 


22- 


•14 


23- 


•46 


24- 


•79 


25- 


• 12 


26- 


•44 


27. 


•77 


28- 


• 09 


29. 


•42 


3o- 


•74 


3i- 


•07 


32- 


• 3 Q 


33- 


•72 


33- 


• o5 


34- 


•37 


35- 


• 70 


36- 


• 02 


3 7 . 


• 35 


38- 


.67 


3 9 . 


• 00 


4o- 


•32 


4i- 


• 65 


42- 


.98 


43- 


•3o 


44. 


•63 


45- 


• 95 


46- 


•28 


47' 



194 c 



Lat. 



■ 83 
.78 
•72 

• 66 

• 61 

• 55 
5o 

•44 

• 38 

• 33 

'27 
22 
16 
11 

• o5 

■99 
H 



• 83 
•77 
•7i 

• 66 

• 6o 
55 

•49 

• 43 

• 38 

•32 

'27 
21 
i5 
10 

.04 

•99 
?3 
J8 

.82 
.76 

•71 
■ 65 

• 6o 
•54 

• 48 

• 43 
■37 

■32 

.26 



Dep. 



Dep. 



Lat. 



701° 



W 



Lat. 



Dep. 



Dep. 



Lat. 



W 



19i 



Lat. 



Dep. 



Dep. 






34 





68 


I 


01 


I 


35 


I 


6q 


2 


o3 


2 


37 


2 


70 


3 


04 


3 


38 


3 


72 


4 


06 


4 


39 


4 


73 


5 


07 


5 


4i 


5 


'74 


6 


08 


6 


42 


6 


76 


7 


•10 


7 


43 


7 


77 


8 


11 


8 


45 


8 


79 


9 


12 


9 


46 


9 


80 


10 


14 


10 


48 


10 


81 


11 


i5 


11 


49 


11 


83 


12 


17 


12 


00 


12 


84 


i3 


18 


i3 


52 


i3 


85 


14 


19 


14 


53 


14 


87 


13 


21 


i5 


54 


i5 


88 


16 


22 


16 


56 


16 


90 



9 
10 

11 

12 
i3 
14 
i5 
16 

18 

J 9 
20 

21 

22 

23 

24 

25 

26 
27 
28 

3o 
3i 

32 

33 
34 
35 
36 

37 
38 
3 9 
40 

4i 
42 
43 

44 
45 
46 

47 
48 

i 9 

5o 



Lat. 



10Y 























Table IV. 




TRAVERSE TABLE. 






125 


g 
& 

3 
(5 
CD 


19° 


19*° 


in° 


19 


1° 


g 

3 
a 
a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


48-22 


16-60 


48-i5 


16-81 


48-07 


17-02 


48-00 


17-23 


5i 


» 52 


49 


17 


16 


93 


49 


09 


17-14 


49 


02 


17 


36 


48 


94 


17 


57 


52 


53 


5o 


11 


17 


26 


5o 


04 


17-47 


49 


96 


17 


69 


49 


88 


17 


9 1 


53 


54 


5i 


06 


17 


58 


5o 


98 


17-80 


5o 


90 


18 


o3 


5o 


82 


18 


25 


54 


55 


52 


00 


17 


9 1 


5i 


92 


i8-i3 


5i 


85 


18 


36 


5i 


76 


18 


39 


55 


56 


52 


9 5 


18 


23 


52 


87 


18-46 


52 


79 


18 


69 


52 


7i 


18 


92 


56 


1 


53 


89 


18 


56 


53 


81 


18.79 


53 


73 


*9 


o3 


53 


65 


*9 


26 


5 7 


54 


84 


18 


88 


54 


76 


19-12 


54 


67 


*9 


36 


54 


5 9 


*9 


60 


58 


5 9 


55 


7I 


l 9 


21 


55 


70 


19-45 


55 


62 


*9 


69 


55 


53 


19 


94 


5 9 


6o 


56 


J 9 


53 


56 


65 


19.78 


56 


56 


20 


o3 


56 


47 


20 


27 


60 


6i 


5 7 


68 


l 9 


86 


57 


5 9 


20-11 


5 7 . 


5o 


20 


36 


57 


4i 


20 


61 


61 


62 


58 


62 


20 


*9 


58 


53 


20 -44 


58 


44 


20 


70 


58 


35 


20 


9 5 


62 


63 


5 9 


5 7 


20 


5i 


5 9 


48 


20-77 


5 9 


3 9 


21 


o3 


5 9 


29 


21 


29 


63 


64 


60 


5i 


20 


84 


60 


42 


21 -10 


60 


33 


21 


36 


60 


24 


21 


63 


64 


65 


61 


46 


21 


16 


61 


37 


21-43 


61 


27 


21 


70 


61 


18 


21 


96 


65 


66 


62 


4o 


21 


49 


62 


3i 


21-76 


62 


21 


22 


o3 


62 


12 


22 


3o 


66 


a 


63 


35 


21 


81 


63 


25 


22-09 


63 


16 


22 


37 


63 


06 


22 


64 


67 


64 


3o 


22 


14 


64 


20 


22-42 


64 


10 


22 


70 


64 


00 


22 


98 


68 


6 9 


65 


24 


22 


46 


65 


U 


22-75 


65 


04 


23 


o3 


64 


94 


23 


32 


69 


70 


66 


19 


22 


79 


66 


09 


23- 08 


65 


98 


23 


37 


65 


88 


23 


65 


70 


71 


67 


i3 


23 


12 


67 


o3 


23-4i 


66 


93 


23 


70 


66 


82 


23 


no 


7i 


7? 


68 


08 


23- 


44 


67 


97 


23-74 


67 


87 


24 


o3 


67 


76 


24 


33 


72 


73 


69 


02 


23 


77 


68 


92 


24-07 


68 


81 


24 


37 


68 


7i 


24 


67 


73 


^ 


69 


97 


24 


09 


69 


86 


24-4o 


69 


76 


24 


70 


69 


65 


25 


01 


74 


7 5 


70 


91 


24 


42 


70 


81 


24-73 


70 


70 


25 


04 


70 


5 9 


20 


34 


75 


76 


7i 


86 


24 


74 


7i 


75 


25-o6 


7i 


64 


25 


37 


7i 


53 


23 


68 


76 


u 


72 


80 


25 


07 


72 


69 


25-39 


72 


58 


25 


70 


72 


47 


26 


02 


9 


78 


73 


75 


25 


3 9 


73 


64 


25-72 


73 


53 


26 


04 


73 


41 


26 


36 


19 


74 


70 


25 


72 


74 


58 


26-o5 


74 


47 


26 


37 


74 


35 


26 


70 


I 9 


80 


75 


64 


26 


o5 


75 


53 


26-38 


75 


41 


26 


70 


75 


29 


27 


o3 


80 


81 


76 


5 9 


26 


37 


76 


47 


26.70 


76 


35 


27 


04 


76 


24 


27 


37 


81 


82 


77 


53 


26 


70 


77 


42 


27. o3 


77 


3o 


27 


37 


77 


18 


2 1 


7i 


82 


83 


78 


48 


27 


02 


78 


36 


27-36 


78 


24 


27 


7i 


78 


• 12 


28 


• o5 


83 


84 


79 


42 


27 


35 


79 


3o 


27-69 


79 


18 


28 


04 


79 


• 06 


28 


• 3 9 


84 


85 


80 


37 


27 


67 


80 


25 


28-02 


80 


12 


28 


37 


80 


00 


28 


.72 


85 


86 


81 


3i 


28 


00 


81 


J 9 


28-35 


81 


07 


28 


71 


80 


.94 


29 


.06 


86 


8 l 


82 


26 


28 


32 


82 


14 


28-68 


82 


01 


29 


04 


81 


• 88 


29 


•40 


87 


88 


83 


21 


28 


65 


83 


08 


29-01 


82 


9 5 


29 


37 


82 


■ 82 


29 


•74 


88 


89 


84 


i5 


23 


to 


84 


02 


29-34 


83 


90 


29 


7i 


83 


.76 


3o 


■07 


89 


90 


85 


10 


29 


84 


97 


29-67 


84 


84 


3o 


04 


84 


■71 


3o 


■4i 


90 


9 1 


86 


04 


29 


63 


85 


91 


3o-oo 


85 


78 


3o 


38 


85 


• 65 


3o 


75 


9 1 


92 


86 


99 


29 


9 5 


86 


86 


3o-33 


86 


72 


3o 


7i 


86 


•5 9 


3i 


09 


9? 


9 3 


87 


93 


3o 


28 


87 


80 


3o-66 


87 


67 


3i 


04 


87 


• 53 


3i 


43 


9 3 


94 


88 


88 


3o 


60 


88 


74 


30-99 


88 


61 


3i 


38 


88 


■47 


3i 


76 


94 


9 5 


89 


82 


3o 


93 


89 


69 


3i-32 


89 


55 


3i 


7i 


89 


•4i 


32 


10 


9 5 


96 


90 


'77 


3i 


■25 


90 


63 


3i-65 


90 


49 


32 


o5 


90 


35 


32 


44 


96 


97 


9 1 


.72 


3i 


58 


9i 


58 


31-98 


9 1 


44 


32 


38 


9 1 


29 


32 


78 


97 


98 


92 


•66 


3i 


■91 


92 


52 


32-3i 


92 


38 


32 


7i 


92 


24 


33 


12 


98 


99 


9 3 


■61 


32 


•23 


9 3 


46 


32-64 


93 


32 


33 


o5 


93 


18 


33 


45 


99 


100 


94-55 


32-56 


94-41 


32-97 


94-26 


33-38 


94-12 


33-79 


100 




s 

P 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Distance. 


1 


L° 


70 


1° 


70 


h° 


70 


1° 



126 



TRAVERSE TABLE. 



Table IV. 



9 
10 

ii 

12 

i3 
U 
i5 

16 

18 
19 

20 

21 
22 
23 
24 
25 
26 

27 

28 

I 9 

3o 
3i 

32 

33 
34 
35 
36 

37 
38 
3 9 
4o 

4i 
42 
43 
44 
45 
46 

47 
48 

to 



20 c 



Lat. 



82 
76 
70 
64 

58 

02 
46 
40 

34 
28 
2 2 
16 
10 

04 

97 
91 

85 

79 

73 
67 
61 
55 

49 
43 

3i 

25 

19 

i3 
07 

01 
9 5 

I 

77 
7i 
65 
5 9 

53 

47 
4i 
35 

2 9 

23 

17 

II 

04 



Dep. 



Dep. 



Lat. 



70< 



20i c 



Lat. 



.34 


0- 


• 68 


i- 


• o3 


2- 


• 3 7 


3- 


•7i 


4- 


•03 


&• 


.39 


6- 


•74 


7- 


•08 


8- 


•42 


9* 


.76 


10- 


•10 


ii- 


•45 


12- 


•79 


i3- 


•i3 


i4- 


•47 


i5- 


•81 


i5- 


•16 


16. 


• 5o 


n- 


•84 


18- 


.18 


19. 


•52 


20- 


.87 


21- 


•21 


22- 


• 55 


23- 


.89 


24- 


•23 


2b- 


• 58 


26- 


•92 


27- 


• 26 


28- 


• 60 


29. 


•94 


3o- 


:3 


Jo- 


3i- 


•97 


32- 


•3i 


33- 


• 65 


34- 


• 00 


35- 


•34 


36- 


•68 


3 7 . 


• 02 


38- 


• 36 


3 9 . 


.71 


4o- 


•o5 


4i- 


.39 


42- 


• 7 3 


43- 


• 07 


44. 


•42 


45- 


.76 


45- 


• 10 


46- 



Si 
.75 

.69 

■ 63 

■5 7 

• 5i 

•44 

• 38 

•32 

26 
20 
i3 

•07 

• 01 

• 9 5 
.89 
•83 
.76 

.70 

• 64 

• 58 

■52 

•45 

• 3 9 

• 33 

'27 

21 

i5 



■02 
.96 
.90 

• 84 
•77 
■7i 

• 65 

■ 5 9 

■ 53 

■47 

• 40 

• 34 
■28 

■22 

16 

•09 

•03 

'97 
.91 



Dep. 



Dep. 



Lat. 



691° 



20£ c 



20| c 



Lat. 



Dep. 



Dep. 



Lat. 



Dep. 



35 

70 
o5 
40 
75 
10 
45 
80 
i5 
5o 

85 
20 
55 
90 

23 
60 
9 5 

3o 
65 



35 
70 
o5 
4o 
76 
11 
46 
81 
16 
5i 

86 
21 

56 

9 l 
2b 

61 

96 

3 1 

66 

01 

36 

7i 
06 

4i 
76 
11 
46 
81 
16 
5i 



10 
11 
12 
i3 
14 
14 
i5 
16 

\l 

*9 
20 
21 
22 

23 

24 

25 

26 

27 
28 

28 

It 

3i 

32 

33 
34 
35 
36 
37 

38. 
3 9 . 
40. 
41 

42 
43 
43 
44 
45 
46 



)4 

s 7 
h 

74 
68 
61 
55 
48 
42 
35 

29 
22 
16 
09 

06 
96 

i3 

77 
70 

64 

57 
5i 

44 
38 
3i 

25 

18 
12 
o5 

99 

92 
86 

?S 

66 
60 
54 
47 
4i 

34 
28 
21 
i5 
08 
02 
o5 

8? 

76 



35 

7i 
06 
42 

77 
i3 
48 
83 

I 9 
54 

25 

61 
96 
3i 

67 
02 
38 
73 
09 

■44 

i5 

5o 
86 
21 

57 
92 

27 
63 



34 

69 
o5 

40 

75 

11 

46 
82 
17 

53 
88 

23 

5 9 

3o 
65 
01 
36 

7i 



9 
10 

11 
12 
i3 
14 
i5 
16 

18 

19 
20 

21 
22 

23 

24 

25 

26 
27 
28 

I 9 

3o 
3i 

32 

33 
34 
35 
36 

37 
38 

39 

4o 

4i 
42 
43 
44 
45 
46 

47 

48 

to 



Lat. 



Dep. 



Lat. 



69£ c 



Table IV. 




TRAVERSE TABLE. 




121 


g 

Sa- 


20° 


20^ 


-° 


20i° 


20f° 


m 

3 
a 
a* 


to 

(3 

fl> 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


47-92 


17-44 


47-85 


17-65 


47-77 


17-86 


47-69 


18.07 


5i 


52 


48-86 


17.79 


48 


79 


18 


00 


48 


71 


18 


21 


48- 


63 


18 


42 


52 


53 


49-80 


18. i3 


49 


72 


18 


34 


49 


64 


18 


56 


49- 


56 


18 


78 


53 


54 


5o-74 


18-47 


5o 


66 


18 


69 


5o 


58 


18 


9 1 


5o 


5o 


J 9 


i3 


54 


55 


5i-68 


18. 81 


5i 


60 


J 9 


04 


5i 


52 


l 9 


26 


5i- 


43 


J 9 


49 


55 


56 


52-62 


19- 15 


52 


54 


l 9 


38 


52 


45 


J 9 


61 


52- 


37 


*9 


84 


56 


5 7 


53-56 


i9-5o 


53 


48 


J 9 


73 


53 


39 


J 9 


96 


53- 


3o 


20 


19 


5 7 


58 


54 -5o 


19-84 


54 


42 


20- 


07 


54 


33 


20 


3i 


54 


24 


20 


55 


58 


5 9 


55-44 


20-18 


55 


35 


20- 


42 


55 


26 


20 


66 


55 


n 


20 


90 


59 


6o 


56-38 


20-52 


56- 


29 


20- 


77 


56 


20 


21 


01 


56- 


11 


21 


26 


60 


6i 


57-32 


20-86 


57 


23 


21 • 


11 


5 7 


14 


21 


36 


57 


04 


21 


61 


61 


62 


58-26 


21-21 


58 


n 


21- 


46 


58 


07 


21 


7 1 


5 7 


98 


21 


97 


62 


63 


59-20 


21-55 


5 9 


11 


21 


81 


5 9 


01 


22 


06 


58- 


91 


22 


32 


63 


64 


60-14 


21-89 


60 


04 


22 


i5 


5 9 


9 5 


22 


41 


5 9 


85 


22 


67 


64 


65 


61.08 


22-23 


60 


98 


22 


5o 


60 


88 


22 


76 


60 


78 


23 


o3 


65 


66 


62-02 


22-57 


61 


92 


22 


84 


61 


82 


23 


11 


61 • 


72 


23 


38 


66 


67 


62-96 


22-92 


62 


86 


23 


J 9 


62 


76 


23 


46 


62 


65 


23 


74 


67 


68 


63- 90 


23-26 


63 


80 


23 


54 


63 


69 


23 


81 


63- 


5 9 


24 


09 


68 


69 


64-84 


23-6o 


64 


74 


23 


88 


64 


63 


24 


16 


64 


52 


24 


45 


69 


70 


65- 78 


23-94 


65 


67 


24 


23 


65 


57- 


24 


5i 


65 


46 


24 


80 


70 


7i 


66-72 


24-28 


66 


61 


24 


57 


66 


5o 


24 


86 


66 


3 9 


25 


i5 


7i 


72 


67-66 


24-63 


67 


55 


24 


92 


67 


44 


25 


21 


67 


33 


25 


5i 


72 


73 


68- 60 


24-97 


68 


49 


25 


27 


68 


38 


25 


5 7 


68 


26 


25 


86 


73 


74 


69.54 


25-3i 


69 


43 


25 


61 


69 


3i 


25 


92 


69 


20 


26 


22 


74 


75 


70-48 


25-65 


70 


36 


25 


96 


70 


25 


26 


27 


70 


14 


26 


5 7 


7 f 


76 


71-42 


25-99 


7i 


3o 


26 


3o 


7i 


.*9 


26 


62 


7i 


07 


26 


9;* 


76 


77 


72-36 


26-34 


72 


24 


26 


65 


72 


12 


26 


97 


72 


01 


27 


28 


]l 


78 


73-3o 


26-68 


73 


18 


27 


00 


73 


06 


27 


32 


72 


94 


27 


63 


ll 


74-24 


27-02 


74 


12 


27 


34 


74 


00 


27 


67 


73 


88 


27 


99 


I 9 


75.18 


27-36 


7 5 


06 


27 


69 


74 


93 


28 


02 


74 


81 


28 


34 


80 


81 


76-12 


27-70 


7 5 


99 


28 


04 


75 


87 


28 


37 


75 


7 5 


28 


.70 


81 


82 


77-o5 


28- o5 


76 


o3 


28 


38 


76 


81 


28 


72 


76 


68 


29 


• o5 


82 


83 


77-99 


28-39 


77 


»7 


28 


73 


77 


•74 


29 


07 


77 


62 


29 


•41 


83 


84 


78-93 


28-73 


78 


81 


29 


07 


78 


68 


29 


•42 


78 


55 


^ 


.76 


84 


85 


79-87 


29-07 


79 


75 


29 


42 


79 


• 62 


29 


77 


79 


49 


3o 


•11 


85 


86 


8o-8i 


29-41 


80 


68 


29 


'77 


80 


■ 55 


3o 


• 12 


80 


42 


3o 


•47 


86 


ll 


8i- 7 5 


29-76 


81 


.62 


3o 


•11 


81 


•49 


3o 


•47 


81 


36 


3o 


•82 


ll 


82-69 


3o-io 


82 


■ 56 


3o 


-46 


82 


•43 


3o 


.82 


82 


29 


3i 


•18 


89 


83-63 


3o-44 


83 


-5o 


3o 


■ 80 


83 


-36 


3i 


•17 


83 


23 


3i 


•53 


89 


90 


84- 5 7 


30-78 


84 


•44 


3i 


• i5 


84 


-3o 


3i 


•52 


84 


16 


3i 


.89 


90 


9 1 


85-5i 


3l«I2 


85 


• 38 


3i 


• 5o 


85 


•24 


3i 


•87 


85 


•10 


32 


•24 


9 1 


92 


86-45 


3i-47 


86 


•3i 


3i 


• 84 


86 


•n 


32 


• 22 


86 


o3 


32 


-5 9 


92 


9 3 


87.39 


3i-8i 


87 


-25 


32 


■ 19 


87 


• 11 


32 


• 5 7 


86 


97 


32 


- 9 5 


9 3 


94 


88-33 


32-i5 


88 


•19 


32 


•54 


88 


•o5 


32 


92 


87 


90 


33 


-3o 


94 


9 5 


89-27 


32-49 


89 


• i3 


32 


• 88 


88 


.98 


33 


• 27 


88 


-84 


33 


-66 


9 5 


96 


90-21 


32-83 


90 


• 07 


33 


•23 


89 


• 92 


33 


• 62 


89 


77 


34 


• 01 


96 


H 


91 -i5 


33-i8 


9i 


• 00 


33 


-5 7 


90 


-86 


33 


97 


90 


.71 


34 


-3 7 


9 Z 


92-00 


33-52 


9 1 


•94 


33 


.92 


9 1 


•79 


34 


•32 


9 1 


64 


34 


.72 


98 


99 


93-o3 


33-86 


92 


• 88 


34 


■27 


92 


• 7 3 


34 


67 


92 


58 


35 


07 


99 


100 


93-97 


34-20 


93-82 


34-6i 


9 3-6 7 


35-02 


93 -5i 


35-43 


100 


6 

a 

03 
m 

5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


00 


S3 
rt 

OD 

n 


H 


)° 


69 


1° 


69£° 


69i° 



128 






TRAVERSE TABLE. 




Table IV. 


g 

a 

a 


21 





2U° 


21£° 


21 


t° 


55' 

3 
n 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


093 


o-36 


0-93 


o-36 


0-93 


0.37 


o- 9 3 


0-37 


I 


2 


I.87 


0-72 


1-86 


0- 


72 


1-86 


0-73 


1 


86 


0- 


74 


2 


3 


2-80 


1-08 


2-80 


i- 


09 


2-79 


1-10 


2 


79 


1 


II 


3 


4 


3.73 


1-43 


3- 7 3 


i- 


45 


3-72 


1-47 


3 


72 


1 


48 


4 


5 


4-67 


1-79 


4-66 


1 


81 


4-65 


1-83 


4 


64 


1 


85 


5 


6 


5.60 


2-l5 


5-5 9 


2- 


n 


5-58 


2-20 


5 


5 7 


2 


22 


6 


7 


6-54 


2-5l 


6-52 


2 


54 


6-5i 


2-57 


6 


5o 


2 


5 9 


7 


8 


7-47 


2-87 


7-46 


2 


90 


7-44 


2-93 


7 


43 


2 


06 


8 


9 


8-4o 


3-23 


8-3 9 


3 


26 


8-37 


3-3o 


8 


36 


3 


34 


9 


10 


9-34 


3-58 


9-32 


3 


62 


9-3o 


3.67 


9 


29 


3 


7i 


10 


ii 


10-27 


3.94 


10-25 


3 


99 


10-23 


4-o3 


10 


22 


4 


08 


11 


12 


11-20 


4-3o 


II. 18 


4 


35 


11-17 


4-4o 


11 


i5 


4 


45 


12 


i3 


12- 14 


4-66 


12-12 


4 


71 


12-10 


4-76 


12 


07 


4 


82 


i3 


14 


i3-07 


5-02 


i3-o5 


5 


07 


i3o3 


5-i3 


i3 


00 


5 


19 


14 


i5 


14-00 


5-38 


13.98 


5 


44 


13-96 


5-5o 


i3 


93 


5 


56 


i5 


16 


14-94 


5.73 


14.91 


5 


80 


14-89 


5-86 


14 


86 


5 


2 3 


16 


I? 


i5-8 7 


6-09 


i5-84 


6 


16 


i5-82 


6-23 


i5 


79 


6 


3o 


17 


16.80 


6,45 


16-78 


6 


52 


i6- 7 5 


6-6o 


16 


7 2 


6 


67 


18 


19 


n-74 


681 


17.71 


6 


89 


17-68 


6-96 


n 


65 


7 


04 


x 9 


20 


18-67 


7.17 


18-64 


7 


23 


18-61 


7-33 


18 


58 


7 


41 


20 


21 


19-61 


7-53 


19.57 


7 


6l 


I9-54 


7.70 


l 9 


5o 


7 


78 


21 


22 


20-54 


7.88 


20- 5o 


7 


97 


20-47 


8-o6 


20 


-43 


8 


• i5 


22 


23 


21-47 


8-24 


21-44 


8 


34 


21.40 


8-43 


21 


-36 


8 


•52 


23 


24 


22-41 


8-6o 


22-37 


8 


70 


22-33 


8-8o 


22 


• 29 


8 


.89 


24 


25 


23-34 


8-96 


23-3o 


9 


06 


23.26 


9-16 


23 


• 22 


9 


• 26 


25 


26 


24-27 


9-32 


24-23 


9 


42 


24-19 


9-53 


24 


■ i5 


9 


• 63 


26 


27 


25-21 


9.68 


25-i6 


9 


79 


25-12 


9.90 


25 


.08 


10 


• 01 


27 


28 


26-14 


10 -o3 


26-10 


10 


i5 


26 -o5 


10-26 


26 


• 01 


10 


•38 


28 


29 


27-07 


10-39 


27 -o3 


10 


5i 


26-98 


10-63 


26 


9 4 


10 


■75 


29 


3o 


28-01 


10-75 


27-96 


10 


87 


27-91 


11-00 


27 


-86 


11 


12 


3o 


3i 


28.94 


ii-ii 


28-89 


11 


24 


28-84 


11-36 


28 


79 


11 


49 


3i 


32 


29-87 


n-47 


29-82 


11 


60 


29-77 


ii- 7 3 


29 


72 


11 


86 


32 


33 


3o-8i 


n-83 


30-76 


11 


96 


30-70 


12-09 


3o 


65 


12 


23 


33 


34 


3i-74 


12-18 


3 1 • 69 


12 


32 


3 1 • 63 


12-46 


3i 


-58 


12 


• 60 


34 


35 


32-68 


12-54 


32-62 


12 


69 


32-56 


12-83 


32 


■ 5i 


12 


•97 


35 


36 


33-6i 


12-90 


33-55 


i3 


o5 


33-5o 


i3 • 19 


33 


•44 


i3 


• 34 


36 


37 


34-54 


i3-26 


34-48 


i3 


41 


34-43 


i3-56 


34 


■37 


i3 


•7i 


37 


38 


35-48 


i3-62 


35-42 


i3 


77 


35-36 


i3- 9 3 


35 


•29 


14 


.08 


38 


3 9 


36-41 


13.98 


36-35 


14 


■14 


36-29 


14-29 


36 


• 22 


14 


■45 


3 9 


4o 


37.34 


14-33 


37.28 


14 


-5o 


37-22 


14-66 


37 


• i5 


14 


■ 82 


4o 


4i 


38-28 


14.69 
i5-oo 


38-21 


14 


• 86 


38-i5 


i5-o3 


38 


-08 


i5 


• 19 


4i 


42 


39-21 


3 9 -i4 


i5 


■22 


39-08 


i5-3 9 


39 


•01 


i5 


■ 56 


42 


43 


40-14 


i5-4i 


4o- 08 


i5 


-58 


4o-oi 


15-76 


3 9 


.94 


i5 


■93 


43 


44 


41-08 


15.77 


4i-oi 


i5 


•9 5 


4o- 94 


i6-i3 


40 


.87 


16 


■ 3o 


44 


45 


42-01 


i6-i3 


41 -q4 


16 


-3i 


41-87 


16-49 


41 


■ 80 


16 


-68 


45 


46 


42-94 


16 -48 


42-87 


16 


.67 


42 • 80 


16 -86 


42 


•73 


17 


o5 


46 


47 


43-88 


16-84 


43- 80 


n 


• o3 


43-73 


17-23 


43 


■ 65 


17 


■42 


47 


48 


44-8i 


17-20 


44-74 


17 


• 40 


44-66 


i7-5 9 


44 


• 58 


n 


79 


48 


49 


45-75 


17-56 


45-67 


17 


.76 


45-59 


17-96 


45 


• 5i 


18 


16 


49 


5o 


46-68 


17.92 


46-60 


18. 12 


46-52 


18-33 


46-44 


i8-53 


JO 




a 

5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 



5 
c 
6 
5 

3 


6 


9° 


68 


!° 


68 


i° 


68 


1° 



Table IV. 




TRAVERSE TABLE. 






129 


a 

to 

3 

a 

CD 


21° 


2H° 


2H° 


21|° 




5a' 

f» 

3 
O 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


47*6l 


18-28 


47-53 


18.48 


47-45 


18-69 


47-37 


18-90 


5i 


52 


48 


55 


18 


64 


48 


46 


18 


85 


48 


38 


l 9 


06 


48 


3o 


19 


27 


52 


53 


49 


48 


18 


99 


4 9 


4o 


l 9 


21 


49 


3i 


l 9 


42 


49 


23 


l 9 


64 


53 


54 


5o 


4i 


l 9 


35 


5o 


33 


1 9 


57 


5o 


24 


r 9 


79 


5o 


16 


20 


01 


54 


55 


5i 


35 


l 9 


7 1 


5i 


26 


*9 


93 


5i 


n 


20 


16 


5i 


08 


20 


38 


55 


56 


02 


28 


20 


07 


52 


r 9 


20 


3o 


52 


10 


20 


52 


52 


01 


20 


75 


56 


5 7 


53 


21 


20 


43 


53 


12 


20 


66 


53 


o3 


20 


89 


52 


94 


21 


12 


5 7 


58 


54 


i5 


20 


79 


54 


06 


21 


02 


53 


96 


21 


26 


53 


87 


21 


49 


58 


5 9 


55. 


08 


21 


14 


54 


99 


21 


38 


54 


89 


21 


62 


54 


80 


21 


86 


59 


6o 


56- 


01 


21 


5o 


55 


92 


21 


75 


55 


83 


21 


99 


55 


73 


22 


23 


60 


6i 


56 


9 5 


21 


86 


56 


85 


22 


11 


56 


76 


22 


36 


56 


66 


22 


60 


61 


» 62 


5 7 • 


88 


22 


22 


5 7 


78 


22 


47 


57 


69 


22 


72 


57 


5 9 


22 


97 


62 


63 


58- 


82 


22 


58 


58 


72 


22 


83 


58 


62 


23 


09 


58 


52 


23 


35 


63 


64 


5 9 . 


75 


22 


94 


5 9 


65 


23 


20 


5 9 


55 


23 


46 


5 9 


44 


23 


72 


64 


65 


60. 


68 


23 


29 


60 


58 


23 


56 


60 


48 


23 


82 


60 


37 


24 


09 


65 


66 


61. 


62 


23 


6D 


61 


5i 


23 


92 


61 


41 


24 


l 9 


61 


3o 


24 


46 


66 


67 


62- 


55 


24 


01 


62 


44 


24 


28 


62 


34 


24 


56 


62 


23 


24 


83 


67 


68 


63- 


48 


24 


37 


63 


38 


24 


65 


63 


2 7 


24 


92 


63 


16 


25 


20 


68 


69 


64- 


42 


24 


73 


64 


3i 


25 


01 


64 


20 


25 


29 


64 


09 


25 


57 


69 


7° 


65- 


35 


25 


09 


65 


24 


25 


37 


65 


i3 


25 


66 


65 


02 


25 


9 4 


70 


71 


66 


28 


25 


44 


66 


n 


25 


73 


66 


06 


26 


02 


65 


95 


26 


3i 


7i 


72 


67. 


22 


25 


80 


67 


10 


26 


10 


66 


99 


26 


3 9 


66 


87 


26 


68 


72 


73 


68 


i5 


26 


16 


68 


04 


26 


46 


67 


92 


26 


75 


67 


80 


27 


o5 


73 


74 


69 


08 


26 


52 


68 


97 


26 


82 


68 


85 


27 


12 


68 


73 


27 


42 


74 


75 


70. 


02 


26 


88 


69 


90 


27 


18 


69 


78 


27 


49 


69 


66 


27 


79 


75 


76 


70 


o5 


27 


24 


70 


83 


27 


55 


70 


7i 


27 


85 


70 


5 9 


28 


16 


76 


77 


71- 


89 


27 


5 9 


7i 


76 


27 


91 


7i 


64 


28 


22 


7i 


52 


28 


'53 


77 


78 


72- 


82 


27 


95 


72 


70 


28 


27 


72 


57 


28 


5o 


72 


45 


28 


90 


78 


S 


73 


75 


28 


3i 


73 


63 


28 


63 


73 


5o 


28 


95 


73 


38 


29 


27 


7,9 


74 


69 


28 


67 


74 


56 


29 


00 


74 


43 


29 


32 


74 


3o 


29 


64 


80 


81 


75 


62 


29 


o3 


75 


49 


29 


36 


75 


36 


29 


69 


75 


23 


3o 


02 


81 


82 


76 


55 


29 


39 


76 


42 


29 


72 


76 


29 


3o 


o5 


76 


16 


3o 


39 


82 


83 


77 


49 


29 


74 


77 


36 


3o 


08 


77 


22 


3o 


42 


77 


09 


3o 


76 


83 


84 


78 


42 


3o 


10 


78 


29 


3o 


44 


78 


16 


3o 


79 


78 


02 


3i 


i3 


84 


85 


79 


35 


3o 


46 


79 


22 


3o 


81 


79 


09 


3i 


i5 


78 


9^ 


3i 


5o 


85 


86 


80 


29 


3o 


82 


80 


i5 


3i 


17 


80 


02 


3i 


52 


79 


88 


3i 


87 


86 


87 


81 


22 


3i 


18 


81 


08 


3i 


53 


80 


9 5 


3i 


89 


80 


81 


32 


24 


87 


88 


82 


16 


3i 


54 


82 


02 


3i 


89 


81 


88 


32 


25 


81 


74 


32 


61 


88 


89 


83 


09 


3i 


89 


82 


95 


32 


26 


82 


81 


32 


62 


82 


66 


32 


98 


89 


90 


84 


02 


32 


25 


83 


88 


32 


62 


83 


74 


32 


99 


83 


5 9 


33 


35 


90 


9 1 


84 


96 


32 


61 


84 


81 


32 


98 


84 


67 


33 


35 


84 


52 


33 


72 


9 1 


92 


85 


89 


32 


97 


85 


74 


33 


34 


85 


60 


33 


72 


85 


45 


34 


09 


92 


9 3 


86 


82 


33 


33 


86 


68 


33 


7 1 


86 


53 


34 


08 


86 


38 


34 


46 


93 


94 


87 


76 


33 


69 


87 


61 


34 


07 


87 


46 


34 


45 


87 


3i 


34 


83 


94 


95 


88 


69 


34 


04 


88 


54 


34 


43 


88 


39 


34 


82 


88 


24 


35 


20 


9j 


96 


89 


.62 


34 


.40 


89 


47 


34 


79 


89 


32 


35 


18 


89 


H 


35 


57 


96 


97 


90 


• 56 


34 


.76 


90 


4o 


35 


16 


90 


25 


35 


55 


90 


09 


35 


94 


9 l 


98 


9 1 


•49 


35 


•12 


9 1 


34 


35 


52 


9i 


18 


35 


9 l 


9 1 


02 


36 


3i 


98 


99 


92 


•42 


35 


• 48 


-9 2 


27 


35 


88 


92 


II 


36 


28 


91 


95 


36 


69 


99 


100 


9 3-36 


35-84 


93-20 


36-24 


93-04 


36-65 


92-88 


37-06 


100 





a 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




a 

a 

a 

03 

Q 


6 


3° 


68 


1° 


68 


h° 


68 


k° 


















i 


>* 



















130 






TRAVERSE TABLE. 




Table IV. 


i 

(5 
P 


2S 


,0 


22i° 


22|° 


22 


1° 





Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


o-o3 


0.37 


0-93 


o-38 


0-92 


0-38 


0-o2 


0-39 


I 


2 


i -85 


0-75 


1-85 


0-76 


1-85 


0-77 


1-84 


o-77 


2 


3 


2-78 


I-I2 


2.78 


I-I4 


2-77 


i-i5 


2-77 


i- 16 


3 


4 


3.71 


i -5o 


3.70 


i-5i 


3.70 


1-53 


3-69 


1 -55- 


4 


5 


4-64 


1.87 


4-63 


1-89 


4-62 


I-OI 


4-6i 


1.93 


5 


6 


5-56 


2-25 


5-55 


2-27 


5-54 


2-3o 


5-53 


2-32 


6 


7 


6-49 


2-62 


6.48 


2-65 


6-47 


2-68 


6-46 


2-71 


7 


8 


7-42 


3-oo 


7-4o 


3-o3 


7-3 9 


3-o6 


7-38 


3-0 9 


8 


9 


8-34 


3.37 


8-33 


3-4i 


8-3i 


3-44 


8-3o 


3-48 


9 


10 


9.27 


3.75 


9.26 


3-79 


9-24 


3-83 


9. 22 


3-87 


10 


ii 


10-20 


4-12 


10.18 


4-H 


10-16 


4-21 


10-14 


4-25 


11 


12 


ii-i3 


4-5o 


11. 11 


4-54 


11-09 


4-59 


11-07 


4-64 


12 


i3 


12 -o5 


4-8 7 


I2>o3 


4-92 


12-01 


4-97 


11.99 


5-o3 


i3 


U 


I2-o8 


5-24 


12.96 


5-3o 


12-93 


5-36 


12-91 


5-4i 


14 


i5 


i3..oi 


5-62 


i3-88 


5-68 


13.86 


5-74 


13-83 


5-8o 


i5 


16 


14-83 


5-99 


14-81 


6-o6 


14-78 


6-12 


14-76 


6-19 


16 


17 


i5- 7 6 


6-37 


15.73 


6-44 


i5 -71 


6-5i 


i5-68 


6-5 7 


17 


18 


16-69 


6-74 


16-66 


6-82 


i6-63 


6-89 


16-60 


6-96 


18 


»9 


17-62 


7-12 


I7-59 


7-19 


17-55 


7-27 


17-52 


7-35 


*9 


20 


18-54 


7'49 


18. 5i 


7-5 7 


18-48 


7-65 


18.44 


7.73 


20 


21 


19-47 


7.87 


19-44 


7- 9 5 


19-40 


8-04 


19.37 


8-12 


21 


22 


20- 40 


8-24 


20-36 


8-33 


20-33 


8-42 


20-29 


8-5i 


22 


23 


21-33 


8-62 


21-29 


8.71 


21-25 


8-8o 


21-21 


8-89 


23 


24 


22-25 


8-99 


22-21 


9.09 


22-17 


9-18 


22-l3 


9-28 


24 


25 


23-l8 


9-37 


23-14 


9-47 


23-10 


9-57 


23 -o5 


9-67 


25 


26 


24-n 


9-74 


24-o6 


9.84 


24-02 


9- 9 5 


23 -98 


io-o5 


26 


27 


25 -o3 


IO-II 


24-99 


10-22 


24-94 


io-33 


24-QO 


10-44 


27 


28 


25.96 


10-49 


25-92 


10- 60 


25-87 


10-72 


25-82 


io-83 


28 


29 


26-89 


10-86 


26-84 


IO- 9 8 


26-79 


II-IO 


26-74 


11-21 


29 


3o 


27-82 


11-24 


27.77 


n-36 


27-72 


-ai-48 


27-67 


11 -6o 


3o 


3i 


28-74 


ii-6i 


28-69 


n-74 


28-64 


11.86 


28.59 


n-99 


3i 


32 


29-67 


n-99 


29-62 


12-12 


29-56 


12-25 


29-51 


12-37 


32 


33 


3o-6o 


12-36 


3o-54 


12 -5o 


3o-49 


12-63 


3o-43 


12-76 


33 


34 


3i-52 


12-74 


3i-47 


I2-87 


3i-4i 


i3-oi 


3i-35 


i3-i5 


34 


35 


32-45 


i3-ii 


32-39 


i3-25 


32-34 


i3-3 9 


32-28 


13-53 


35 


36 


33-38 


13-49 


33-32 


13-63 


33-26 


i3- 7 8 


33-20 


13-92 


36 


37 


34-3i 


13-86 


34-24 


14-01 


34-i8 


14-16 


34-12 


i4-3i 


37 


38 


35-23 


14-24 


35-17 


i4-3 9 


35-u 


14-54 


35-04 


14-70 


38 


39 


36-i6 


14-61 


36-io 


14-77 


36- o3 


14-92 


35.97 


i5-o8 


3 9 


4o 


37.09 


14-98 


37-02 


i5-i5 


36 -96 


i5-3i 


36 .89 


i5-47 


40 


4i 


38-01 


15-36 


37.95 


i5-52 


37-88 


i5-6 9 


3 7 -8i 


15-86 


4i 


42 


38- 9 4 


i5- 7 3 


38-87 


15-90 


38- 80 


16-07 


38-73 


16-24 


42 


43 


39-87 


i6-ii 


3 9 -8o 


16-28 


3 9 -73 


16-46 


3 9 -65 


16. 63 


43 


44 


4o- 80 


16-48 


40-72 


16-66 


4o-65 


16-84 


40-58 


17-02 


44 


45 


41-72 


16-86 


4i-65 


17-04 


41-57 


17-22 


41 -5o 


i7-4o 


45 


46 


42-65 


17-23 


42-57 


17-42 


42 -5o 


17-60 


42-42 


17-79 


46 


47 


43-58 


17-61 


43 -5o 


17-80 


43-42 


17-99 


43-34 


18.18 


47 


48 


44-5o 


17-98 


44-43 


18-18 


44-35 


18-37 


44-27 


18-56 


48 


49 


45-43 


18. 36 


45-35 


i8-55 


45-27 


18-75 


45-19 


i8- 9 5 


49 


5o 


46-36 


18-73 


46-28 


i8- 9 3 


46-19 


19-13 


46-n 


19.34 


5o 


Distance. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


O 

C 

ca 

00 

5 


6 


8° 


671° 


67i° 


67 


4° 







































• 

Table IV. 




TRAVERSE TABLE. 






131 


b 

! pj 

a 


22° 


22i° 


22i° 


22 


3.0 


s 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


! 5i 


47-29 


19-10 


47-20 


I9-3l 


47-12 


19-52 


47 -o3 


19-72 


5i 


52 


48-21 


19-48 


48- 13 


19-69 


48-04 


19-90 


47-95 


20-11 


52 


■ 53 


49-14 


19-85 


49 -o5 


20-07 


48-97 


20-28 


48-88 


20 -5o 


53 


: 54 


50-07 


20-23 


49-98 


20-45 


49-89 


20-66 


49-80 


20-88 


54 


55 


5i-oo 


20- 60 


50-90 


20-83 


5o-8i 


21 -o5 


50-72 


21-27 


55 


56 


51-92 


20-98 


5i-83 


21-20 


5i-74 


21-43 


5i-64 


21-66 


56 


57 


52-85 


21-35 


52-76 


21-58 


52-66 


2I-8l 


52-57 


22-04 


57 


58 


53-78 


21-73 


53-68 


21-96 


53- 5 9 


22-20 


53-49 


22-43 


58 


5 9 


54-70 


22-10 


54-6i 


22-34 


54-5i 


22-58 


54-4i 


22-82 


5 9 


6o 


55-63 


22-48 


55-53 


22-72 


55-43 


22-96 


55-33 


23-20 


60 


6i 


56-56 


22-85 


56-47 


23-10 


56-36 


23-34 


56-25 


23- 5o 


61 


62 


57.49 


23-23 


5 7 -38 


23-48 


57-28 


23.73 


57-18 


23.98 


62 


63 


58-41 


23-6o 


58-3i 


23-85 


58- 20 


24-*i 


58-io 


24-36 


63 


64 


5 9 -34 


23-97 


59-23 


24-23 


59-13 


?4-49 


59-02 


24-75 


64 


65 


60-27 


24-35 


60-16 


24-61 


60 -o5 


24-8 7 


59-94 


25-i4 


65 


66 


61-19 


24-72 


61 -09 


24-99 


60-98 25-26 


60-87 


25-52 


66 


67 


62-12 


25-10 


62-01 


25-37 


61-90 


25-64 


61-79 


25.91 


67 


68 


63 -o5 


25-47 


62-94 


25-75 


62-82 


26-02 


62-71 


26-3o 


68 


69 


63- 9 8 


25-85 


63-86 


26- 13 


63-75 


26-41 


63-63 


26-68 


69 


70 


64-90 


26-22 


64-79 


26-5i 


64-67 


26-79 


64-55 


27-07 


70 


7i 


65-83 


26-60 


65.71 


ro-88 


65- 60 


27.17 


65-48 


27-46 


7i 


72 


66.76 


26-97 


66-64 


27-26 


66-52 


27-55 


66-40 


27-84 


72 


73 


67.68 


27-35 


67.^ 


27-64 


67-44 


27-94 


67-32 


28-23 


73 


74 


68-6i 


27-72 


68-49 


28-02 


68-37 


28-32 


68-24 


28-62 


74 


75 


69-54 


28-10 


59-42 


28-40 


69-29 


28-70 


69.17 


29-00 


75 


76 


70.47 


28-47 


70-34 


28-78 


70-21 


29-08 


70-09 


29-39 


76 


77 


7I-39 


28-84 


71-27 


29.16 


7i-i4 


29-47 


71-01 


29-78 


77 


78 


72-32 


29-22 


72-19 


29-53 


72-06 


29 -85 


71-93 


3o- 16 


78 


79 


73-25 


29-5 9 


73-12 


29-91 


72-99 


3o-23 


72-85 


3o-55 


79 


80 


74-17 


29-97 


74-04 


30-29 


73.91 


3o-6i 


73.78 


30-94 


80 


81 


7510 


3o-34 


74-97 


30-67 


74-83 


3i -oo 


74-70 


3i-32 


81 


82 


70 -o3 


30-72 


75-89 


3i -o5 


75.76 


3i-38 


75-62 


3i«7i 


82 


83 


76-96 


3i-09 


76-82 


3i-43 


76-68 


3i- 7 6 


76-54 


32- 10 


83 


84 


77.88 


3i-47 


77- 7 5 


3i-8i 


77-61 


32-i5 


77.46 


32-48 


84 


85 


78-81 


3i-84 


78-67 


32-19 


78-53 


32-53 


78.39 


32-8 7 


85 


86 


79-74 


32-22 


79-60 


32-56 


79-45 


32-91 


79-3i 


33-26 


86 


87 


80 -66 


32-59 


8o- 52 


32-94 


80 -38 


33-29 


8o-23 


33-64 


87 


88 


8i-5 9 


32-97 


81 -45 


33-32 


81. 3o 


33-68 


8i-i5 


34 -o3 


88 


89 


82-52 


33-34 


82-37 


33-70 


82-23 


34- 06 


82-08 


34-42 


89 


90 


83-45 


33-71 


83- 3o 


34-o8 


83- 15 


34-44 


83-oo 


34- 80 


90 


9 1 


84-37 


34-09 


84-22 


34-46 


84-07 


34-82 


83.92 


35-19 


9 1 


92 


85 -3o 


34-46 


85- 15 


34-84 


85-00 


35-21 


84-84 


35-58 


92 


9 3 


86-23 


34-84 


86- 08 


35-21 


85-92 


35.59 


85.76 


35-96 


9 3 


94 


87-16 


35-21 


87-00 


35.59 


86-84 


35.97 


86-69 


36-35 


94 


95 


88- 08 


35.59 


87-93 


35.97 


87-77 


36-35 


87-61 


36.74 


95 


96 


89-01 


35-96 


88-85 


36-35 


88-69 


36-74 


88-53 


37-12 - 


96 


97 


8 9 - 9 4 


36-34 


89.78 


36- 7 3 


89-62 


37-12 


89-45 


3 7 - 5i 


97 


98 


9 o-86 


36.71 


90-70 


37- 11 


90-54 


37-00 


90-38 


37-90 


98 


99 


91-79 


37-09 


91 -63 


37-49 


91-46 


37-89 


9i-3o 


38-28 


99 


100 


92-72 


37.46 


92-55 


37.86 


92-39 


38-2 7 


92-22 


38-67 


100 


6 
a 

a 

S 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


0) 



si 

5 


6£ 





67 


10 

4 


1 

67£° 


67 


*° 



















1 


' 
















1 

! 


132 






TRAVERSE TABLE. 




Table IV. 


o 

9 
a 
to 


11 





23^° 


23£° 


23 


1° 


g 

3 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


0-92 


0.39 


0-92 


0-39 


0-92 


o«4o 


0.92 


0-40 


I 


2 


1-84 


O.78 


1.84 


0-79 


1-83 


o-8o 


1*83 


0-8l 


2 


3 


2-76 


1-17 


2-76 


1-18 


2-75 


1-20 


2-75 


I- 21 


3 


4 


3-68 


1-56 


3-68 


i-58 


3-6 7 


1-59 


3-66 


I- 61 


4 


5 


4-6o 


1-95 


4- 5 9 


1-97 


4.59. 


1.99 


4-58 


2-01 


5 


6 


5-52 


2-34 


5-5i 


2-3 7 


5-5o 


2-39 


5-49 


2-42 


6 


I 


6-44 


2-74 


6-43 


2-76 


6-42 


2-79 


6.41 


2-82 


I 


7-36 


3-i3 


7-35 


3-i6 


7-34 


3-19 


7-32 


3-22 


9 


8-28 


3-52 


8-27 


3-55 


8-25 


3-5 9 


8-24 


3-62 


9 1 


IO 


9-20 


3-91 


9.19 


3- 9 5 


9-17 


3-99 


9"i5 


4-o3 





II 


io-i3 


4-3o 


10-11 


4.34 


1 • 09 


4-3 9 


10-07 
10-98 


4.43 


11 


12 


11 -o5 


4-6 9 


u-o3 


4-74 


II -00 


4-78 


4-83 


12 


i3 


11.97 


5-o8 


11.94 

12-0t> 


5-i3 


II-Q2 


5-f8 


n-oo 


5-24 


i3 


i4 


12-89 


5.47 


5-53 


I 2 • «4 


5-58 


I2-8I 


5-64 


14 


i5 


i3-8i 


5-86 


13.78 


5.92 


13-76 


5-98 


i3-73 


6-o4 


i5 


16 


14-73 


6-25 


14-70 


6-32 


14-67 


6-38 


14-64 


6-44 


16 


17 


i5-65 


6-64 


i5-62 


671 


i5- 5o 


6-78 


i5-56 


6-85 


17 


18 


i6-5 7 


7-o3 


i6-54 


7. 11 


16. 5i 


7-18 


16.48 


7-25 


10 


19 


17.49 


7-42 


17-46 


7«5o 


17-42 

i8-34 


7-58 


17-39 


7-65 


-9 


20 


18.41 


7.81 


18. 38 


7.89 


7-97 


18. 3i 


8-o5 


20 


21 


19.33 


8-21 


19-29 


8-29 


19. 2C 


8.37 


19-22 


8-46 


21 


22 


20-25 


8-6o 


20-21 


8-68 


20-l8 


8-77 


20-14 


8-86 


22 


23 


21.17 


8-99 


21*l3 


9.08 


21-09 


^■17 


21 -o5 


9-26 


23 


24 


22-09 


9-38 


22-05 


9-47 


22-01 


9-5 7 


21-97 


9.67 


24 


25 


23-01 


9-77 


22-07 


9.87 


22-93 


9-97 
10-37 


22-88 


10-07 


25 


26 


23-93 
24-85 


10-16 


23 -89 


10-26 


23-84 


23.80 


10-47 


26 


27 


10-55 


24'8l 


10-66 


24.76 


10-77 


24.71 


10-87 


27 


20 


25.77 


I0 -9f 
n-33 


25.73 


ii-o5 


25-68 


11 • 16 


25-<>3 


11-28 


20 


29 


26-69 


26-64 


u-45 


26-59 


n-56 


26-54 


u-68 


29 


3o 


27-62 


11-72 


27-56 


n-84 


27-51 


11-96 


27-46 


12-08 


36 


3i 


28-54 


12-11 


28-48 


12-24 


28-43 


12-36 


28.37 


12-49 


3i 


32 


29.46 


12 -5o 


29-40 


12-63 


29.35 


12-76 


29-29 


12-89 


32 


33 


3o-38 


12-89 


3o-32 


i3-o3 


3o-26 


i3-i6 


30-21 


i3-29 


33 


34 


3i-3o 


13-28 


3i-24 


i3-42 


3i'.i8 


13-56 


3l-I2 


i3-6 9 


34 


35 


32-22 


13-68 


32.16 


i3-82 


32-10 


i3- 9 6 


32-o4 


i4-io 


35 


36 


33-14 


14-07 


33.o8 


14-21 


33-oi' 


14-35 


32- 9 5 


i4-5o 


36 


37 


34- 06 


14-46 


34-00 


i4-6i 


33-93 


14-7^ 


33-87 


14-90 


37 


38 


34-98 


14-85 


34-91 


1 5- 00 


34-85 


i5-i5 


34-78 


i5-3o 


38 


3 9 


35.90 


i5-24 


35-83 


i5-3 9 


35-77 


i5-55 


35.70 


i5-7i 


39 


4o 


36-82 


15-63 


36-75 


i5. 79 


36-68 


i5-95 


36-6i 


16. h 


40 


4i 


37-74 


l6-02 


37-67 


16. 18 


37-60 


i6-35 


37.53 


16. 5i 


4i 


42 


38-66 


16-41 


38- 5 9 


16. 58 


38-52 


i6- 7 5 


38-44 


16.92 
17.32 


42 


43 


3 9 -58 


16.80 


39>5i 


16.97 


3 9 -43 


17. i5 


3 9 - 36 


43 


44 


40 -5o 


17-19 


4o-43 


17.37 


4o-35 


17-54 


40-27 


17.72 


44 


45 


41-42 


17-58 


4i-35 


17-76 


41-27 


17.94 


41-19 


18-12 


45 


46 


42-34 


J 7-97 


42-26 


18. 16 


42-18 


18.34 


42-10 


18-53 


46 


47 


43-26 


18-36 


43.i8 


i8.55 


43-io 


18-74 


43-02 


19.33 


47 


48 


44- 18 


18-76 


44-io 


i8-o5 


44-02 


19-14 


43-93 


48 


i 9 


45-io 


19-15 


45-02 


19.34 


44-94 


19.54 


44-85 


19.73 


49 


5o 


46- o3 


19.54 


45-94 


19.74 


45-85 


19-94 


45.77 


20-14 


5o 


6 


a 
a 

5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 

a 

Q 


6 


7° 


66 


|° 


66i° 


66 


4° 





















Table IV. 




TRAVERSE TABLE. 






133 


I 

3" 

3 

a 


23° 


234° 


23i° 


23 1° 




3 
C5 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


46.95 


19-93 


46-86 


20-l3 


46.77 


20-34 


46-68 


20-54 


5i 


52 


47 


87 


20 


32 


47 


78 


20-53 


47 


69 


20-73 


47 


60 


20 


94 


52 


53 


48 


79 


20 


71 


48 


70 


20-G2 


48 


60 


2I-l3 


48 


5i 


21 


35 


53 


54 


49 


7i 


21 


10 


49 


61 


21-32 


49 


52 


21-53 


49 


43 


21 


73 


54 


55 


5o 


63 


21 


49 


5o 


53 


21-71 


5o 


44 


2I-o3 


5o 


34 


22 


i5 


55 


56 


5i 


55 


21 


88 


5i 


45 


22-11 


5i 


36 


22-33 


5i 


26 


22 


55 


56 


57 


52 


47 


22 


27 


52 


37 


22 -5o 


52 


27 


22-73 


52 


*7 


22 


96 


57 


58 


53 


39 


22 


66 


53 


29 


22-90 


53 


19 


23- 1 3 


53 


09 


23 


36 


58 


5 9 


54 


3i 


23 


o5 


54 


21 


23-29 


54 


11 


23-53 


54 


00 


23 


.76 


5 9 


6o 


55 


23 


23 


44 


55 


i3 


23-68 


55 


02 


23-92 


54 


92 


24 


.16 


60 


6i 


56 


i5 


23 


83 


56 


o5 


24-08 


55 


94 


24-32 


55 


83 


24 


57 


61 


62 


57 


07 


24 


23 


56 


97 


24-47 


56 


86 


24-72 


56 


75 


24 


97 


62 


63 


57 


99 


24 


62 


57 


88 


24-87 


57 


77 


25-12 


57 


66 


25 


37 


63 


64 


58 


91 


25 


01 


58 


80 


25-26 


58 


69 


25-52 


58 


58 


25 


78 


64 


65 


5 9 


83 


25 


40 


5 9 


72 


25-66 


5 9 


6i 


25-92 


5 9 


5o 


26 


18 


65 


66 


60 


75 


25 


79 


60 


64 


26-o5 


60 


53 


26-32 


60 


4i 


26 


58 


66 


67 


61 


67 


26 


18 


61 


56 


26-45 


61 


44 


26-72 


61 


33 


26 


98 


67 


68 


62 


5 9 


26 


57 


62 


48 


26-84 


62 


36 


27-11 


62 


24 


27 


39 


68 


69 


63 


5i 


26 


96 


63 


40 


27-24 


63 


28 


27-5i 


63 


16 


27 


79 


69 


70 


64 


44 


27 


35 


64 


32 


27-63 


64 


*9 


27-91 


64 


07 


28 


19 


70 


V 


65 


36 


27 


74 


65 


23 


28- o3 


65 


11 


28- 3i 


64 


99 


28 


5 9 


7 1 


72 


66 


28 


28 


i3 


66 


i5 


28-42 


66 


o3 


28-71 


65 


90 


29 


00 


72 


73 


67 


20 


28 


52 


67 


07 


28-82 


66 


9 5 


29-11 


66 


82 


29 


4o 


73 


74 


68 


12 


28 


9i 


67 


99 


29-21 


67 


86 


29-51 


67 


73 


29 


80 


74 


7 ? 


69 


04 


29 


3o 


68 


9 1 


29-61 


68 


78 


29-91 


68 


65 


3o 


21 


7 5 


76 


69 


96 


29 


70 


69 


83 


3o-oo 


69 


70 


3o-3o 


69 


56 


3o 


61 


76 


7 2 


70 


88 


3o 


09 


70 


75 


3o-4o 


70 


61 


30-70 


70 


48 


3i 


01 


7 I 


78 


7i 


80 


3o 


48 


7i 


67 


3o-79 


7i 


53 


3i -io 


7i 


39 


3i 


4i 


78 


7,9 


72 


72 


3o 


87 


72 


58 


3i-i8 


72 


45 


3i -5o 


72 


3i 


3i 


82 


l 9 o 


80 


73 


64 


3i 


26 


73 


5o 


3i-58 


73 


36 


31-90 


73 


22 


32 


22 


81 


74 


56 


3i 


65 


74 


42 


31.97 


74 


28 


32-3o 


74 


14 


32 


62 


81 


82 


75 


48 


32 


04 


75 


34 


32-37 


7 5 


20 


32-70 


75 


06 


33 


o3 


82 


83 


76 


4o 


32 


43 


76 


26 


32-76 


76 


12 


33-io 


75 


97 


33 


43 


83 


84 


77 


32 


32 


82 


77 


18 


33-16 


77 


o3 


33-49 


76 


89 


33 


83 


84 


85 


78 


24 


33 


21 


78 


10 


33-55 


77 


o5 


33.89 


77 


80 


34 


23 


85 


86 


79 


16 


33 


60 


79 


02 


33- 9 5 


78 


87 


34-29 


78 


.72 


34 


64 


86 


87 


80 


08 


33 


99 


S 


9 3 ■ 


34-34 


79 


78 


34-69 


79 


63 


35 


04 


87 


88 


81 


00 


34 


38 


85 


34-74 


80 


70 


35-09 


80 


55 


35 


44 


88 


89 


81 


92 


34 


78 


81 


77 


35-i3_ 


81 


62 


35.49 


81 


46 


35 


84 


89 


90 


82 


85 


35 


17 


82 


69 


35-53 


82 


54 


35.89 


82 


38 


36 


25 


90 


9 1 


83 


77 


35 


56 


83 


61 


35-92 
36-32 


83 


45 


36-29 


83 


29 


36 


65 


9 1 


92 


84 


69 


35 


9 5 


84 


53 


84 


37 


36-68 


84 


21 


37 


o5 


92 


93 


85 


61 


36 


34 


85 


45 


36-71 


85 


29 


37-08 


85 


12 


37 


46 


93 


94 


86 


53 


36 


73 


86 


37 


37-11 


86 


20 


37.48 


86 


04 


37 


86 


94 


9 5 


87 


45 


37 


12 


87 


29 


37 -5o 


87 


12 


37-88 


86 


9 5 


38 


26 


9, 5 


96 


88 


37 


37 


5i 


88 


20 


37-90 


88 


04 


38-28 


87 


«7 


38 


66 


96 


97 


89 


29 


37 


90 


89 


12 


38-29 


88 


o5 


38-68 


88 


79 


39 


07 


97 


98 


90 


21 


38 


29 


90 


04 


38-68 


89 


87 


39-08 


89 


70 


3 9 


47 


98 


99 


9 1 


i3 


38 


68 


90 


96 


3 9 -o8 


90 


79 


39.48 


90 


62 


3 9 


87 


99 


100 


92 -o5 


39-07 


91-88 


39-47 


91.71 


39.87 


91-53 


40-27 


100 


6 


a 

.2 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


i i 


6> 


r° 


66|° 


66 


i° 


66 


1° 





















134 



TRAVERSE TABLE. 



Table IV. 



24° 



24£< 



Lat. 



Dep. 



Lat. 



9 

IO 

II 

12 

i3 
14 
i5 
16 

17 
18 

19 
20 

21 
22 

23 

24 

25 

26 
27 
28 

11 

3i 

32 

33 
34 
35 
36 

37 
38 
3 9 
4o 

4i 
42 
43 
44 
45 
46 

47 
48 
49 
5a 



10 
10 
11 
12 
i3 
U 
i5 
16 

17 
18 

19 
20 
21 

21 
22 

23 

24 

25 

26 
27 

28 
29 

3o- 

3i 

3i 

32 

33 
34- 
35 
36 

37 

38 

3 9 

40 

4i 

42 

42 

43 

44. 

45 



9i 

83 

74 
65 
5 7 
48 
3 9 
3i 
22 
14 

o5 
96 
88 

79 
70 
62 
53 
44 
36 
27 

18 
10 
01 

9 3 

84 
7 5 
67 
58 

49 
4i 

32 
23 

i5 

06 
97 

it 

71 

63 
54 

46 

37 
28 
20 
11 
02 
Q4 
85 

76 
68 



4i 
81 
22 

63 
o3 

44 
85 

25 

66 
07 

47 
88 
29 
69 
10 
5i 

& 

73 
i3 

54 
9 5 
35 
76 

17 
58 
98 

^ 
80 

20 

61 
02 
42 
83 
24 
64 
o5 
46 
86 
.27 

68 
08 

49 
90 
3o 

71 
12 

52 

93 

34 



IO 
10 

II 

12 

i3 

U 
i5 

16 

17 
18 

19 

20 
20 
21 
22 

23 

24 

25 

26 
27 

28 
29 

3o 
3i 
3i 

32 

33 
34 
35 
36 

37 
38 

3 9 
4o 

4i 
41 

42 
43 
44 
45 



Dep. 



Lat. 



Dep. 



Dep. 



Lat. 



66 c 



65| c 



24i c 



Lat. 



Dep. 



Dep. 






4i 


0- 





83 


I- 


I 


24 


2- 


I 


66 


3- 


2 


07 


4- 


2 


49 


5. 


2 


90 


6- 


3 


32 


7- 


3 


73 


8- 


4 


i5 


9- 


4 


56 


9- 


4 


98 


10- 


5 


3 9 


ii- 


5 


81 


12- 


6 


22 


i3- 


6 


64 


i4- 


7 


o5 


i5- 


7 


46 


16. 


7 


88 


3: 


8 


29 


8 


71 


19. 


9 


12 


19. 


Q 


54 


20- 


9 


95 


21- 


10 


37 


22- 


10 


78 


23- 


II 


20 


24- 


11 


61 


25- 


12 


o3 


26- 


12 


44 


27. 


12 


86 


28- 


i3 


,27 


29. 


i3 


68 


29- 


14 


10 


3o- 


14 


5i 


3i- 


14 


93 


32- 


i5 


• 34 


33- 


i5 


.76 


34- 


16 


•17 


35- 


16 


• 5 9 


36- 


17 


00 


3 7 . 


17 


42 


38- 


n 


83 


39- 


18 


25 


39- 


18 


66 


40. 


19 


08 


4i- 


19 


49 


42- 


19 


£ 


43- 


20 


44. 


20 


73 


45- 



Lat. 



65i c 



24|° 



Lat. 



Dep. 



91 

•82 
.72 

• 63 
•54 
■45 

■ 36 
•27 

l l 

• 08 

■99 

30 

h 

■71 
.62 

• 53 
■44 
•35 

25 

16 
.07 

.& 

• 70 
•61 

52 

.43 
.34 

H 

i5 
.06 

n 

38 
.78 
.69 
•6o 

■ 5i 
•42 
■33 

23 

14. 

• o5 
)6 
*1 

■11 

• 68 

to 

•41 



42 
84 
26 

67 

5i 

93 
35 

77 
l 9 

61 
02 
44 
86 
28 
70 
12 
54 
9 5 

3 7 

79 
21 
63 
o5 

'47 
89 
3o 
72 
14 
56 

98 
40 
82 

23 

65 
07 

49 
91 
33 

75 

16 
58 
00 
42 
84 
26 
68 
10 
5i 
9 3 



1 
2 

3 
4 
5 
6 

7 
8 

9 
10 

11 
12 
i3 
14 
i5 
16 

17 
18 

19 
20 

21 

22 

23 
24 
25 

26 

27 
28 

29 

3o 
3.1 

32 

33 
34 
35 
36 

37 
38 
3 9 
40 

41 
42 
43 
44 
45 
46 

47 
48 

£ 



Dep. 



Lati 



65i< 



Table IV. 


TRAVERSE TABLE. 




135 


Ed' 

u 

S 
C5 
? 


24° 


24} 


-° 


24i° 


24£° 


g 

3 


? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


46-5g 


20-74 


46 -5o 


20-9D 


46-41 


2l-l5 


46-32 


21-35 


5i 


52 


47 -5o 


2I-l5 


47 


4i 


21- 


36 


47 


32 


21- 


56 


47-22 


21- 


77 


52 


53 


48-42 


21-56 


48 


32 


21- 


77 


48 


23 


21 


98 


48-i3 


22- 


*9 


53 


54 


49-33 


21-96 


49 


24 


22- 


18 


49 


14 


22 


39 


49-04 


22- 


61 


54 


55 


5o-24 


22-37 


5o- 


i5 


22- 


5 9 


5o 


o5 


22 


81 


49-95 


23- 


o3 


55 


56 


5i-i6 


22-78 


5i- 


06 


23- 


00 


5o 


96 


23 


22 


5o-86 


23- 


44 


56 


57 


52-07 


23-i8 


5i- 


97 


23- 


41 


5i 


87 


23 


64 


5i -76 


23 


86 


5 7 


58 


52-99 


23.59 


52 


88 


23- 


82 


52 


78 


24 


o5 


52-67 


24 


28 


58 


5 9 


53- 90 


24-00 


53- 


79 


24- 


23 


53 


69 


24 


47 


53-58 


24 


70 


5 9 


6o 


54-8i 


24-40 


54- 


7* 


24- 


64 


54 


60 


24 


88 


54-49 


25 


12 


60 


6i 


55.73 


24-8i 


55- 


62 


25- 


o5 


55 


5i 


25 


3o 


55-4o 


25 


54 


61 


62 


56-64 


25-22 


56- 


53 


2D- 


46 


56 


42 


25 


7 1 


56- 3o 


25 


96 


62 


63 


57-55 


25-62 


5 7 - 


44 


25- 


88 


5 7 


33 


26 


i3 


57-21 


26 


38 


63 


64 


58-47 


26 -o3 


58- 


35 


26 


29 


58 


24 


26 


54 


58-12 


26 


79 


64 


65 


5 9 -38 


26.44 


5 9 


26 


26 


70 


5 9 


i5 


26 


96 


59-03 


27 


21 


65 


66 


60-29 


26.84 


60 


18 


27 


11 


60 


06 


27 


37 


59-94 


27 


63 


66 


67 


6l-2I 


27.25 


61 


09 


27 


52 


60 


9J 


27 


78 


60 -85 


28 


o5 


67 


68 


62-12 


27-66 


62 


00 


27- 


93 


61 


88 


28 


20 


61.75 


28 


47 


68 


69 


63 -o3 


28.06 


62 


9 1 


28 


34 


62 


79 


28 


61 


62-66 


28 


89 


69 


70 


63 - 9 5 


28.47 


63 


82 


28. 


75 


63 


70 


29 


o3 


63- 5 7 


29 


3i 


70 


7? 


64-86 


28.88 


64 


74 


29 


16 


64 


61 


29 


44 


64-48 


29 


72 


7i 


72 


65 -78 


29-28 


65 


65 


29 


57 


65 


52 


29 


86 


65- 3 9 


3o 


14 


72 


73 


66-69 


29-69 


66 


56 


29 


98 


66 


43 


3o 


27 


66-29 


3o 


56 


73 


74 


67-60 


3o-io 


67 


47 


3o 


39 


67 


34 


3o 


69 


67-20 


3o 


98 


74 


7 5 


68-52 


3o>5i 


68 


38 


3o 


80 


68 


25 


3i 


10 


68-n 


3i 


40 


7 5 


76 


69-43 


30-91 


69 


29 


3i 


21 


69 


16 


3i 


52 


69-02 


3i 


82 


76 


71 


70-34 


3i-32 


70 


21 


3i 


63 


70 


07 


3i 


93 


69 -o3 


32 


24 


77 


78 


71-26 


3i-73 


7i 


12 


32 


04 


70 


98 


32 


35 


70-84 


32 


66 


78 


79 


72-17 


32-i3 


72 


o3 


32 


45 


7i 


89 


32 


76 


71.74 


33 


07 


29 


80 


73.08 


32-54 


72 


94 


32 


86 


72 


80 


33 


-18 


72-65 


33 


49 


80 


81 


74-00 


32-95 


73 


85 


33 


27 


73 


■71 


33 


5 9 


73-56 


33 


•91 


81 


82 


74-91 


33-35 


74 


76 


33 


68 


74 


.62 


34 


00 


74-47 


34 


•33 


82 


83 


75-82 


33.76 


75 


68 


34 


09 


75 


53 


34 


42 


75-38 


34 


•75 


83 


84 


76.74 


34-17 


76 


5 9 


34 


5o 


76 


•44 


34 


-83 


76-28 


35 


•n 


84 


85 


77-65 


34- 5 7 


77 


5o 


34 


9 1 


77 


■ 35 


35 


■25 


77-19 


35 


•5 9 


85 


86 


78 -56 


34-98 


78 


4i 


35 


32 


78 


• 26 


35 


•66 


78-10 


36 


•00 


86 


ll 


79-48 


35-3 9 


79 


32 


35 


73 


79 


•n 


36 


•08 


79-01 


36 


•42 


87 


8o- 3 9 


35-79 


80 


•24 


36 


■14 


80 


• 08 


36 


•49 


79-92 


36 


•84 


88 


89 


8i-3i 


36-20 


81 


•i5 


36 


-55 


80 


•99 


36 


•91 


80-82 


37 


•26 


89 


90 


82-22 


36-6i 


82 


• 06 


36 


96 


81 


.90 


37 


■32 


81.73 


37 


• 68 


90 


9 1 


83- 13 


37-01 


82 


•97 


37 


38 


82 


• 8i 


37 


•74 


82-64 


38 


• 10 


9 1 


92 


84 -o5 


37.42 


83 


•88 


37 


•79 


83 


• 72 


38 


• i5 


83-55 


38 


•52 


92 


9 3 


84.96 


37-83 


84 


•79 


38 


•20 


84 


• 63 


38 


•57 


84-46 


38 


.94 


93 


94 


85 -87 


38-23 


85 


•7i 


38 


61 


85 


•54 


38 


.98 


85-3 7 


39 


• 35 


94 


9 5 


86-79 


38-64 


86 


•62 


39 


• 02 


86 


•45 


3 9 


•40 


86-27 


39 


•77 


9 5 


96 


87.70 


39-03 


87 


•53 


39 


•43 


87 


•36 


3 9 


•81 


87-18 


40 


.19 


96 


97 


88-6i 


39.45 


88 


•44 


39 


■ 84 


88 


•27 


4o 


•23 


88-09 


40 


• 61 


97 


98 


89.53 


3 9 -86 


89 


•35 


4o 


•25 


89 


•18 


40 


•64 


89-00 


4i 


■ o3 


98 


99 


90-44 


40-27 


90 


•26 


4o 


■66 


90 


•09 


4i 


• o5 


89-91 


4i 


45 


99 


100 


91.35 


40-67 


91-18 


41-07 


91 -00 


41-47 


90-81 


4i-8 7 


100 


6 


e 

er) 

BO 

a 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


09 

V 

c 
a 

Q 


66° 


65 


1° 


65£° 


65i° 



136 






TRAVERSE TABLE. 




Table IV. 


O 

5° 

P 

D 

CD 


25° 


25i° 


25£° 


25 


1° 


d 

3 

a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


O'QI 


0-42 


o-go 


0-43 


0-90 


o-43 


0-90 


o-43 


I 


2 


1 


81 





85 


1 


81 





85 


1 


8i 





86 


I 


80 





87 


2 


3 


2 


72 


I- 


27 


2 


71 


1 


28 


2 


71 


1 


29 


2 


70 


1 


3o 


3 


4 


3 


63 


I 


69 


3 


62 


1 


7i 


3 


61 


1 


72 


3 


60 


1 


74 


4 


5 


4 


53 


2 


11 


4 


52 


2 


i3 


4 


5i 


2 


i5 


4 


5o 


2 


x 7 


5 


6 


5 


44 


2 


54 


5 


43 


2 


56 


5 


42 


2 


58 


5 


4o 


2 


61 


6 


I 


6 


34 


2 


96 


6 


33 


2 


99 


6 


32 


3 


01 


6 


3o 


3 


04 


I 


7 


25 


3 


38 


7 


24 


3 


4i 


7 


22 


3 


44 


7 


21 


3 


48 


9 


8 


16 


3 


80 


8 


14 


3 


84 


8 


12 


3 


87 


8 


11 


3 


9 1 


9 


10 


9 


06 


4 


23 


9 


04 


4 


27 


9 


o3 


4 


3i 


9 


01 


4 


34 


10 


II 


9 


97 


4 


65 


9 


9 5 


4 


69 


9 


9 3 


4 


74 


9 


91 


4 


78 


11 


12 


10 


88 


5 


07 


10 


85 


5 


12 


10 


83 


5 


r 7 


10 


81 


5 


21 


12 


i3 


11 


78 


5 


49 


11 


76 


5 


55 


11 


73 


5 


60 


11 


7i 


5 


65 


i3 


14 


12 


69 


5 


92 


12 


66 


5 


97 


12 


64 


6 


o3 


12 


61 


6 


08 


14 


i5 


i3 


5 9 


6 


34 


i3 


5 7 


6 


40 


i3 


54 


6 


46 


i3 


5i 


6 


52 


i5 


16 


14 


5o 


6 


76 


i4 


47 


6 


83 


14 


44 


6 


89 


14 


41 


6 


o5 


16 


\l 


i5 


4i 


7 


18 


i5 


38 


7 


25 


i5 


34 


7 


32 


i5 


3i 


7 


39 


17 


16 


3i 


7 


61 


16 


28 


7 


68 


16 


25 


7 


75 


16 


21 


7 


82 


18 


*9 


17 


22 


8 


o3 


17 


18 


8 


10 


\l 


i5 


8 


18 


17 


11 


8 


25 


*9 


20 


18 


i3 


8 


45 


18 


09 


8 


53 


o5 


8 


61 


18 


01 


8 


69 


20 


21 


l 9 


o3 


8 


87 


18 


99 


8 


96 


18 


Q 5 


9 


04 


18 


91 


9 


12 


21 


22 


*9 


94 


9 


3o 


19 


2° 


9 


38 


19 


86 


9 


47 


19 


82 


9 


56 


22 


23 


20 


85 


9 


72 


20 


80 


9 


81 


20 


76 


9 


90 


20 


72 


9 


9? 


23 


24 


21 


75 


10 


14 


21 


7 1 


10 


24 


21 


66 


10 


33 


21 


62 


10 


43 


24 


25 


22 


66 


10 


5 7 


22 


61 


10 


66 


22 


56 


10 


76 


22 


52 


10 


86 


25 


26 


23 


56 


10 


99 


23 


52 


11 


09 


23 


47 


11 


19 


23 


42 


11 


3o 


26 


27 


24 


47 


11 


4i 


24 


42 


11 


52 


24 


37 


11 


62 


24 


32 


11 


73 


27 


20 


25 


38 


11 


83 


25 


32 


11 


94 


25 


27 


12 


o5 


25 


22 


12 


16 


28 


29 


26 


28 


12 


26 


26 


23 


12 


37 


26 


11 


12 


48 


26 


12 


12 


60 


29 


3o 


'27 


1? 


12 


68 


27 


i3 


12 


80 


27 


12 


92 


27 


02 


i3 


o3 


3o 


3i 


28 


10 


i3 


10 


28 


04 


i3 


22 


27 


98 


i3 


35 


27 


02 


i3 


47 


3i 


32 


29 


00 


i3 


52 


28 


94 


i3 


65 


28 


88 


i3 


78 


28 


02 


i3 


90 


32 


33 


29 


91 


i3 


o5 


29 


85 


14 


08 


29 


79 


14 


21 


29 


72 


14 


34 


33 


34 


3o 


81 


14 


37 


3o 


7 5 


U 


5o 


3o 


69 


14 


64 


3o 


62 


14 


77 


34 


35 


3i 


72 


14 


79 


-3i 


66 


14 


9 3 


3i 


5 9 


i5 


07 


3i 


52 


i5 


21 


35 


36 


32 


63 


i5 


21 


32 


56 


i5 


36 


32 


49 


i5 


5o 


32 


43 


i5 


64 


36 


37 


33 


53 


i5 


64 


33 


46 


i5 


78 


33 


40 


i5 


9 3 


33 


33 


16 


07 


37 


38 


34 


44 


16 


06 


34 


37 


16 


21 


34 


3o 


16 


36 


34 


23 


16 


5i 


38 


3 9 


35 


35 


16 


48 


35 


27 


16 


64 


35 


20 


16 


79 


35 


i3 


16 


94 


3 9 


4o 


36 


25 


16 


90 


36 


18 


17 


06 


36 


10 


H 


22 


36 


o3 


n 


38 


40 


4i 


37 


16 


J 7 


33 


37 


08 


H 


49 


37 


01 


n 


65 


36 


93 


n 


81 


41 


42 


38 


06 


17 


75 


37 


99 


n 


92 


37 


91 


18 


08 


37 


83 


18 


25 


42 


43 


38 


97 


18 


x 7 


38 


89 


18 


34 


38 


81 


18 


5i 


38 


73 


18 


68 


43 


44 


39 


88 


18 


60 


3 9 


80 


18 


77 


39 


7i 


18 


% 


3 9 


63 


l 9 


12 


44 


45 


4o 


78 


=•9 


02 


4o 


70 


l 9 


20 


40 


62 


J 9 


4o 


53 


19 


55 


45 


46 


4i 


69 


*9 


44 


4i 


6.0 


19 


62 


41 


52 


l 9 


80 


4i 


43 


19 


98 


46 


47 


42 


60 


J 9 


86 


42 


5i 


20 


o5 


42 


42 


20 


23 


42 


33 


20 


42 


47 


48 


43 


5o 


20 


29 


43 


4i 


20 


48 


43 


32 


20 


66 


43 


23 


20 


85 


48 


49 


44 


•4i 


20 


•7i 


44 


32 


20 


go 


44 


23 


21 


10 


44 


i3 


21 


29 


i 9 


5o 


45-32 


21 • i3 


45-22 


21-33 


45 -i3 


21-53 


45 -o3 


21-72 


5o 


Distance. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 






a 




6 


5° 


64 


3.0 


64 


i° . 


64 


i° 


Q 



Table IV. 




TRAVERSE TABLE. 






m 


a 

3 
a 
? 


25° 


25|° 


25i° 


25 


1° 


B 

3 
n 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


46-22 


21-55 


46- 13 


21-75 


46 -o3 


21-96 


45-94 


22-l6 


5i 


52 


47 


i3 


21 


98 


47 


o3 


22 


18 


46 


93 


22-39 


46 


-84 


22-59 


52 


53 


48 


o3 


22 


40 


47 


2 4 


22 


61 


47 


84 


22-82 


47 


•74 


23 -o3 


53 


54 


48 


94 


22 


82 


48 


84 


23 


o3 


48 


■74 


23-25 


48 


• 64 


23-46 


54 


55 


49 


85 


23 


24 


49 


74 


23 


46 


49 


64 


23-68 


49 


•54 


23 -89 


55 


56 


5o 


75 


23 


67 


5o 


65 


23 


89 


5o 


54 


24-11 


5o 


•44 


24-33 


56 


5 7 


5i 


66 


24 


09 


5i 


55 


24 


3i 


5i 


45 


24-54 


5i 


■34 


24-76 


57 


58 


02 


57 


24 


5i 


52 


46 


24 


74 


52 


35 


24-97 


52 


■24 


25-20 


58 


5 9 


53 


47 


24 


9 3 


53 


36 


25 


17 


53 


25 


25-4o 


53 


•14 


25-63 


5 9 


6o 


54 


38 


25 


36 


54 


27 


25 


5 9 


54 


16 


25-83 


54 


•04 


26-07 


60 


6i 


55 


28 


25 


78 


55 


17 


26 


02 


55 


06 


26-26 


54 


Q4 


26-5o 


61 


62 


56 


J 9 


26 


20 


56 


08 


26 


45 


55 


9 6 


26-69 


55 


-84 


26-94 


62 


63 


57 


10 


26 


62 


56 


98 


26 


87 


56 


86 


27-12 


56 


•74 


27-37 


63 


64 


58 


00 


27 


o5 


57 


89 


27 


3o 


5 7 


77 


27-55 


57 


64 


27-80 


64 


65 


58 


91 


27 


47 


58 


79 


27 


73 


58 


67 


27.98 


58 


-55 


28-24 


65 


66 


5 9 


02 


27 


89 


5 9 


69 


28 


i5 


5 9 


5 7 


28-41 


5 9 


45 


28-67 


66 


67 


60 


12 


28 


32 


60 


60 


28 


58 


60 


47 


28-84 


60 


35 


29-11 


67 


68 


61 


63 


28 


74 


61 


5o 


29 


01 


61 


38 


29-27 


61 


-25 


29-54 


68 


69 


62 


54 


29 


16 


62 


4i 


29 


43 


62 


28 


29-71 


62 


i5 


29-98 


69 


70 


63 


44 


29 


58 


63 


3i 


29 


86 


63 


18 


3o-i4 


63 


o5 


3o-4i 


70 


7i 


64 


35 


3o 


01 


64 


22 


3o 


29 


64 


08 


3o-57 


63 


9 5 


3o-85 


7i 


72 


65 


25 


3o 


43 


65 


12 


3o 


7 1 


64 


99 


3 1 -oo 


64 


85 


3i- 2 8 


72 


73 


66- 


16 


3o 


85 


66 


o3 


3! 


14 


65 


89 


3i-43 


65 


7 5 


3i -71 


73 


74 


67 


07 


3i 


27 


66 


9 3 


3i 


57 


66 


79 


3i-86 


66 


65 


32-i5 


74 


75 


67 


97 


3i 


70 


67 


83 


3i 


99 


67 


69 


32-29 


67 


■ 55 


32-58 


75 


76 


68 


88 


32 


12 


68 


74 


32 


42 


68 


60 


32-72 


68 


45 


33-02 


76 


77 


69 


79 


32 


54 


69 


64 


32 


85 


69 


5o 


33- 15 


69 


35 


33-45 


77 


78 


70 


69 


32 


96 


70 


55 


33 


27 


70 


40 


33-58 


70 


25 


33.89 


78 


79 


7i 


60 


33 


39 


7i 


45 


33 


70 


7i 


3o 


34-oi 


7i 


16 


34-32 


79 


80 


72 


5o 


33 


81 


72 


36 


34 


i3 


72 


21 


34-44 


72 


06 


34.76 


80 


81 


73 


41 


34 


23 


73 


26 


34 


55 


73 


11 


34-87 


72 


96 


35-19 


81 


82 


74 


32 


34 


65 


74 


n 


34 


98 


74 


01 


35- 3o 


73 


86 


35-62 


82 


83 


7 5 


22 


35 


08 


75 


07 


35 


4i 


74 


91 


35.73 


74 


76 


36- 06 


83 


84 


76 


i3 


35 


5o 


75 


97 


35 


83 


7 5 


82 


36-i6 


75 


66 


•36-49 


84 


85 


77 


04 


35 


92 


76 


88 


36 


26 


76 


72 


36- 5 9 


76 


56 


36- 9 3 


85 


86 


77 


94 


36 


35 


77 


78 


36 


68 


77 


62 


37-02 


77 


46 


3 7 - 36 


86 


87 


78 


85 


36 


77 


78 


69 


37 


11 


78 


52 


3 7 -45 


78 


36 


37-80 


3 


88 


79 


76 


37 


*9 


79 


5 9 


37 


54 


79 


43 


37-88 


79 


26 


38-23 


89 


80 


66 


37 


61 


80 


5o 


37 


96 


80 


33 


38-32 


80 


16 


38-67 


89 


90 


81 


57 


38 


04 


81 


4o 


38 


3 9 


81 


23 


38-75 


81 


06 


39-10 


90 


9 1 


82 


47 


38 


46 


82 


3i 


38 


82 


82 


14 


39-18 


81 


96 


39.53 


9 1 


92 


83 


38 


38 


88 


83 


21 


39 


24 


83 


04 


39-61 


82 


86 


39.97 


92 


93 


84 


29 


39 


3o 


84 


11 


3 9 


67 


83 


04 


40 -04 


83 


76 


4o -4o 


93 


94 


85 


19 


39 


73 


85 


02 


40 


10 


84 


84 


40-47 


84 


67 


40-84 


94 


95 


86 


10 


4o 


i5 


85 


92 


4o 


52 


85 


75 


40-90 


85 


5 7 


41-27 


9 5 


96 


87 


01 


4o 


57 


86 


83 


40 


9 5 


86 


65 


41-33 


86 


47 


41-71 


96 


97 


87 


9i 


40 


99 


87 


73 


41 


38 


87 


55 


41-76 


87 


37 


42-14 


92 


98 


88 


82 


4i 


42 


88 


64 


4i 


80 


88 


45 


42-19 


88 


27 


42-58 


98 


99 


89 


72 


41 


84 


89 


54 


42 


23 


89 


36 


42-62 


89 


n 


43-oi 


99 


100 


90-63 


42-26 


90-45 


42-66 


90-26 


43 -o5 


90-07 


43-44 


100 






B 
in 

■ s 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




a 

m 

* 3 


61 


»° 


64|° 


64i° 


64- 


\° 



138 






TRAVERSE TABLE. 




Table IV. 


d 

so 
s 
o 


2£ 





26i° 


26i° 


26 


1° 


3 



CD 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


0-90 


o-44 


0-90 


o-44 


0-89 


0-45 


0-8 9 


0-45 


I 


2 


l-8o 


o-88 


1.79 


o-88 


1.79 


0-8 9 


1-79 


0-90 


2 


3 


2-70 


I»32 


2-69 


i-33 


2-68 


1-34 


2-68 


1-35 


3 


4 


3-6o 


1-75 


3-5 9 


1.77 


3-58 


1-78 


3-5 7 


i-8o 


4 


5 


4-49 


2-19 


4.48 


2-21 


4-47 


2-23 


4-46 


2-25 


5 


6 


5-3 9 


2-63 


5-38 


2-65 


5-37 


2-68 


5-36 


2-70 


6 


7 


6-29 


3-07 


6-28 


3-io 


6-26 


3-12 


6-25 


3-i5 


I 


8 


7.19 


3-5i 


7.17 


3-54 


7-16 


3-57 


7-14 


3.6o 


9 


8-09 


3- 9 5 


8-07 


3.98 


8-o5 


4-02 


8-04 


4-o5 


9 


10 


8.99 


4-38 


8. 97 


4-42 


8- 9 5 


4-46 


8- 9 3 


4-5o 


10 


ii 


9.89 


4-82 


9.87 


4-8 7 


9-84 


4-QI 


9.82 


4-95 


11 


12 


10-79 


5-26 


10-76 


5-3i 


10-74 


5-35 


10-72 


5-4o 


12 


i3 


n-68 


5-70 


n-66 


5.75 


u-63 


5-8o 


ii-6i 


5-85 


i3 


14 


12-58 


6-14 


12-56 


6- 19 


12-53 


6-25 


12 -5o 


6-3o 


14 


i5 


i3-48 


6-58 


i3-45 


6-63 


i3-42 


6-69 


i3 .39 


6-75 


i5 


16 


14-38 


7-01 


14-35 


7-08 


14-32 


7-14 


14-20 


7-20 


16 


n 


15-28 


7-45 


i5-25 


7-52 


I5-2I 


7.59 


i5-i8 


7-65 


17 


18 


16.18 


7-80 


16-14 


7.96 


16-11 


8-o3 


16-07 


8-io 


18 


10 


17-08 


8-33 


17-04 


8-40 


17-00 


8-48 


16-97 


8-55 


*9 


20 


17-98 


8-77 


17-94 


8-85 


17.90 


8-92 


17-86 


9-00 


20 


21 


18-87 


9-21 


18. 83 


9.29 


18.79 


9.37 


18.75 


9-45 


21 


22 


19-77 


9-64 


19.73 


9-73 


19-69 


9-82 


19-65 


9.90 


22 


23 


20-67 


10-08 


20-63 


10-17 


20-58 


10-26 


20-54 


10-35 


23 


24 


21-57 


10-52 


21-52 


io-6i 


21-48 


10-71 


21-43 


io-8o 


24 


25 


22-47 


10-96 


22-42 


11 -06 


22-37 


11. i5 


22-32 


11-25 


25 


26 


23-37 


n-4o 


23-32 


11 -5o 


23-27 


11 -6o 


23-22 


11-70 


26 


27 


24-27 


n-84 


24-22 


11-94 


24-16 


12 -o5 


24-n 


I2-l5 


3 


28 


25-17 


12-27 


25-11 


12-38 


25-o6 


12-49 


25-00 


12 -6o 


29 


26-06 


12-71 


26-01 


12-83 


25-95 


12-94 


25-90 


i3-o5 


29 


3o 


26-96 


i3-i5 


26-91 


i3-27 


26-85 


i3-3 9 


26-79 


i3-5o 


3o 


3i 


27-86 


13-59 


27-80 


i3- 7 i 


27-74 


13-83 


27-68 


i3- 9 5 


3i 


32 


28-76 


i4-o3 


28-70 


i4-i5 


28-64 


14-28 


28-58* 


14-40 


32 


33 


29-66 


14-47 


29-60 


i4-6o 


29.53 


14-72 


29-47 


14-85 


33 


34 


3o-56 


14-90 


3o-49 


i5-o4 


3o-43 


i5-i 7 


3o-36 


i5-3o 


34 


35 


3i-46 


i5-34 


3i -39 


i5-48 


3i-32 


i5-62 


3i-25 


i5-75 


35 


36 


32-36 


15.78 


32-29 


15.92 


32-22 


16-06 


32-i5 


16-20 


36 


37 


33-26 


l6-22 


33.i8 


16.36 


33-n 


i6-5i 


33- 04 


16-65 


ll 


38 


34-i5 


16-66 


34-o8 


16. 81 


34-oi 


16-96 


33- 9 3 


17-10 


3 9 


35 -o5 


17-10 


34-98 


17-25 


34-90 


i7-4o 


34-83 


17-55 


39 


40 


35.95 


17.53 


35-87 


17.69 


35- 80 


17-85 


35.72 


18-00 


40 


4i 


36-85 


17.97 


36-77 


18. i3 


36-69 


18-29 


36- 61 


18.45 


41 


42 


37.75 


18-41 


37-67 


18. 58 


37.59 


18-74 


37-5i 


18.90 


42 


43 


38-65 


i8-85 


38-57 


19-02 


38-48 


19-19 


38-4o 


i 9 -35 


43 


44 


3 9 -55 


19-29 


3 9 -46 


19-46 


39-38 


19-63 


3 9 -2 9 


19-80 


44 


45 


4o-45 


19.73 


4o-36 


19-90 


40-27 


20- 08 


40-18 


20-25 


45 


46 


4i-34 


20-17 


41-26 


20-35 


41-17 


20-53 


4i- 08 


20.70 


46 


47 


42-24 


20-60 


42-i5 


20-79 


42-06 


20-97 


4I-Q7 


2I-I5 


47 


48 


43-14 


21-04 


43 -o5 


21-23 


42-96 


21-42 


42-86 


21 -6o 


48 


49 


44.04 


21-48 


43- o5 


21-67 


43-85 


21-86 


43.76 


22-o5 


49 


5o 


44.94 


21-92 


44-84 


22-11 


44-75 


22-3l 


44-65 


22-5o 


5o 


6 


a 
a 

GO 

s 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 

S) 

cs 

M 

GO 

Q 


64° 
1 


63|° 


63 


h° 


63 


\° 



Table IV. 




TRAVERSE TABLE. 




139 


3 
o 
p 


26° 


26i° 


26i° 


26|° 


d 

3 

n 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


45-84 


22-36 


45-74 


22-56 


45-64 


22-76 


45-54 


22-96 


5i 


52 


46 


■74 


22 


80 


46 


64 


23 


00 


46 


54 


23 


20 


46 


43 


23 


4i 


52 


53 


47 


64 


23 


23 


47 


53 


23 


44 


47 


43 


23 


65 


47 


33 


23 


86 


53 


54 


48 


53 


23 


67 


48 


43 


23 


88 


48 


33 


24 


09 


48 


22 


24 


3i 


54 


55 


49 


■43 


24 


II 


49 


33 


24 


33 


49 


22 


24 


54 


49 


11 


24 


76 


55 


56 


5o 


33 


24 


55 


5o 


22 


24 


77 


5o 


12 


24 


99 


5o 


01 


25 


21 


56 


5 7 


5i 


23 


24 


99 


5i 


12 


25 


21 


5i 


01 


25 


43 


5o 


90 


25 


66 


5 7 


58 


52 


i3 


25 


43 


52 


02 


25 


65 


5i 


91 


25 


88 


5i 


79 


26 


11 


58 


5 9 


53 


o3 


25 


86 


52 


9 2 


26 


09 


52 


00 


26 


33 


52 


69 


26 


56 


5 9 


6o 


53 


9 3 


26 


3o 


53 


81 


26 


54 


53 


70 


26 


77 


53 


58 


27 


01 


60 


6i 


54 


83 


26 


74 


54 


71 


26 


98 


54 


5 9 


27 


22 


54 


47 


27 


46 


61 


62 


55 


73 


27 


18 


55 


61 


27 


42 


55 


49 


27 


66 


55 


36 


27 


91 


62 


63 


56 


62 


27 


62 


56 


5o 


27 


86 


56 


38 


28 


11 


56 


26 


28 


36 


63 


64 


5 7 


52 


28 


06 


57 


40 


28 


3i 


57 


28 


28 


56 


5 7 


i5 


28 


81 


64 


65 


58 


42 


28 


49 


58 


3o 


28 


75 


58 


17 


29 


00 


58 


04 


29 


26 


65 


66 


5 9 


32 


28 


9 3 


5 9 


l 9 


29 


3 


5 9 


07 


29 


45 


58 


94 


29 


7\ 


66 


67 


60 


22 


29 


37 


60 


09 


29 


5 9 


96 


29 


90 


5 9 


83 


3o 


16 


67 


68 


61 


12 


29 


81 


60 




3o 


08 


60 


86 


3o 


34 


60 


72 


3o 


61 


68 


69 


62 


02 


3o 


25 


61 


08 


3o 


52 


61 


75 


3o 


79 


61 


62 


3i 


06 


69 


70 


62 


92 


3o 


69 


62 


78 


3o 


96 


62 


65 


3i 


23 


62 


5i 


3i 


5i 


70 


7i 


63 


8l 


3i 


12 


63 


68 


3i 


40 


63 


54 


3i 


68 


63 


4o 


3i 


96 


7i 


72 


64 


71 


3i 


56 


64 


5 7 


3i 


84 


64 


44 


32 


i3 


64 


29 


32 


4i 


72 


73 


65 


6l 


32 


00 


65 


47 


32 


29 


65 


33 


32 


5 7 


65 


10 


32 


86 


73 


74 


66 


5i 


32 


44 


66 


37 


32 


73 


66 


23 


33 


02 


66 


08 


33 


3i 


74 


75 


67 


4i 


32 


88 


67 


27 


33 


17 


67 


12 


33 


46 


66 


97 


33 


76 


75 


76 


68 


3i 


33 


32 


68 


16 


33 


61 


68 


01 


33 


91 


67 


87 


34 


21 


76 


77 


69 


21 


33 


7 5 


69 


06 


34 


06 


68 


9 1 


34 


36 


68 


76 


34 


66 


77 


78 


70 


11 


34 


l 9 


69 


96 


34 


DO 


69 


80 


34 


80 


69 


65 


35 


11 


78 


19 


7i 


00 


34 


63 


70 


85 


34 


94 


70 


70 


35 


25 


70 


55 


35 


56 


7,9 


80 


7i 


90 


35 


07 


7 1 


75 


35 


38 


7i 


5 9 


35 


70 


7i 


44 


36 


01 


80 


81 


72 


80 


35 


5i 


72 


65 


35 


83 


72 


49 


36 


14 


72 


• 33 


36 


46 


81 


82 


73 


70 


35 


9 5 


73 


54 


36 


27 


73 


38 


36 


5 9 


73 


22 


36 


9i 


82 


83 


74 


60 


36 


38 


74 


44 


36 


7 1 


74 


28 


37 


o3 


74 


12 


37 


36 


83 


84 


75 


5o 


36 


82 


• 7 5 


34 


37 


i5 


75 


n 


37 


48 


75 


01 


37 


81 


84 


85 


76 


4o 


37 


26 


76 


23 


37 


5 9 


76 


07 


37 


93 


7 5 


90 


38 


26 


85 


86 


77 


3o 


37 


70 


77 


i3 


38 


04 


76 


96 


38 


37 


76 


00 


38 


7i 


86 


87 


78 


20 


38 


14 


78 


o3 


38 


48 


77 


86 


38 


82 


77 


69 


39 


16 


87 


88 


79 


09 


38 


58 


78 


92 


38 


92 


78 


75 


39 


27 


78 


58 


3 9 


61 


88 


89 


79 


99 


39 


01 


79 


82 


39 


36 


79 


65 


3 9 


7i 


79 


48 


4o 


06 


89 


90 


80 


89 


39 


45 


80 


72 


3 9 


81 


Bo 


54 


4o 


16 


80 


37 


4o 


5i 


90 


9 1 


81 


79 


39 


89 


81 


62 


4o 


25 


81 


44 


40 


60 


81 


26 


4o 


96 


9 1 


92 


82 


69 


4o 


33 


82 


5i 


4o 


69 


82 


33 


4i 


o5 


82 


i5 


4i 


4i 


92 


9 3 


83 


5 9 


4o 


77 


83 


4i 


4i 


i3 


83 


23 


41 


5o 


83 


o5 


41 


86 


93 


94 


84 


49 


4i 


21 


84 


3i 


41 


58 


84 


12 


4i 


94 


83 


94 


42 


3i 


94 


9 5 


85 


39 


4i 


65 


85 


20 


42 


02 


85 


02 


42 


3 9 


84 


83 


42 


76 


95 


96 


86 


28 


42 


08 


86 


10 


42 


46 


85 


91 


42 


83 


85 


73 


43 


21 


96 


97 


87 


18 


42 


52 


87 


00 


42 


90 


86 


81 


43 


28 


86 


62 


43 


66 


9 1 


98 


88 


08 


42 


96 


87 


89 


43 


34 


87 


70 


43 


73 


87 


5i 


44 


11 


98 


99 


88 


98 


43 


40 


88 


79 


43 


79 


88 


60 


44 


17 


88 


40 


44 


56 


99 


100 


89-88 


43-84 


89-69 


44-23 


89.49 


44-62 


89 -3o 


45-oi 


100 


O 

a 

on 

S 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


£ 

a 

a 

i 


64° 


63 


r 


63 


h° 


63i° 



140 



TRAVERSE TABLE. 



Table IV. 



27 ( 



27i c 



2n c 



27f c 



Lat. 



Dep. 



Lat. 



Dep. 



Lat. 



Dep. 



Lat. 



Dep. 



9 
10 

ii 

12 

i3 

14 
i5 
16 

17 
18 

19 
20 

21 

22 

23 
24 
25 

26 

3 
12 

3i 

32 

33 
34 
35 
36 
37 
38 
3 9 
4o 

41 
42 
43 
44 
45 
46 

47 
48 

to 



9 
10 
11 
12 
i3 
14 
i5 
16 
16 

n 

18 

19 
20 

21 

22 

23 
24' 

24 

25 

26 

27 
28 
29 

3o 
3i 

32 
32 

33 
34 
35 

36 

37 
38 
3 9 
4o 
46 
4i 
42 
43 
44 



7° 
67 
56 
45 
35 
24 
i3 
02 
9 1 

80 
69 
58 
'47 
3 7 
26 
i5 
04 
o3 
82 

7i 
60 

49 

38 
28 

06 
9 5 

84 
73 

62 
5i 
40 
29 
19 
08 

97 
56 
7 5 
64 

53 

42 
3i 
20 



45 

9i 
36 

82 
27 
72 
18 
63 

2 9 
54 

99 
45 
90 
36 
81 
26 
72 

17 
63 

08 

53 

99 
44 
90 
35 

80 
26 

7i 

62 



77 
66 

55 



44 

?9 
34 
80 

25 

71 
16 

■ 6i 
07 

52 

98 

43 

88 
34 
79 

25 

70 



9 
10 
11 
12 

i3 

14 
i5 
16 
16 

18 

19 
20 

21 

22 

23 

24 
24 

25 

26 

27 
28 
29 

3o 

3i 

32 
32 

33 
34 
35 

36 

37 

38 

3 9 

40 

40. 

4i 

42 

43 

44 



70 
67 

56 
45 
33 
22 
11 
00 
.89 

78 
■ 67 
56 
45 
34 
22 
11 
00 



67 
56 
45 
34 

23 

11 

00 

89 
78 
67 

56 

45 
34 

23 

12 



78 
67 

56 

45 

34 

23 

12 



78 

67 
56 
45 



46 
92 

37 
83 

75 
21 
66 
12 
58 

04 

49 
9^ 
41 

87 
33 

78 
24 
70 
16 

62 
07 
53 

99 
45 
90 
36 
82 
28 
74 

6? 
11 

57 
o3 
48 
9 4 
4o 
86 
3i 

'77 

23 

69 
i5 
60 
06 

52 

.98 
■44 

.89 



o 
I 
2 

3 

4 
5 
6 

7 

7 
8 

9 

10 

11 

12 

i3 
U 
i5 
i5 
16 

18 
19 
20 
21 

22 

23 
23 

24 

25 

26 

27 
28 

29 

3o 
3i 
3i 

32 

33 
34 
35 

36 

37 
38 

39 
3 9 

4o 

4i 

42 
43 
44 



89 

77 
66 
55 
44 

32 

21 
10 

98 
87 

76 
64 
53 
42 
3i 
19 
08 

97 
85 

74 

63 
5i 

40 
29 
10 
06 
9 5 
84 
72 
61 

5o 
38 
27 
16 
o5 
9 3 
82 

7i 
5o 

48 
37 

25 

14 

o3 

02 
00 
69 
58 
46 
35 



46 
92 

ll 

3i 

77 

23 

69 
16 

62 

08 
54 
00 

46 

£ 

85 
3i 
■77 

23 

70 
16 
62 
08 
54 
01 

47 
o3 

3 9 
85 

3i 
78 
24 
70' 
16 
62 
08 
55 
01 
47 

93 
3q 
86 

32 

78 

24 

70 
16 

63 
09 



9 
10 

11 

12 
i3 
14 
i5 
i5 
16 

18 

19 

20 
21 
22 

23 
23 

24 

25 

26 

27 
28 
29 

3o 
3o 
3i 

32 

33 
34 
35 

36. 

37 
38 
38 
3 9 
40 
4i 
42 
43 
44. 



77 
65 

54 
42 
3i 

19 
00 
06 
85 

73 
62 
5o 

3 9 
27 
16 
04 
>3 
5'j 
70 

58 

47 
35 
24 
12 
01 
80 
78 
66 
55 

43 

32 

20 
09 

>7 
56 

74 
63 
5i 
40 

28 

o5 
94 

82 

7i 
5 9 
48 
36 

25 



'9 
[ 9 
20 
20 
20 
21 
21 
22 
22 

23 



47 
93 

40 

86 
33 

79 
26 

72 

19 
66 

12 
5o 
o5 

52 

9 ^ 

4D 

92 
38 
85 
3i 

■78 
24 
7i 
17 
64 
11 
5 7 
04 
5o 

97 

43 
90 

3 7 
83 
3o 
76 

23 

16 

62 
09 

56 
02 

9 5 
42 
88 
35 
82 
28 



Dep. 



Lat. 



Dep. 



Lat. 



Dep. 



Lat. 



Dep. 



Lat. 



63< 



62i c 



62}< 



Table IV. 




TRAVERSE TABLE. 


141 


9 


o 
? 


27° 


27i° 


2H° 


2?f° 


e 

5" 
a 

? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


45-44 


23-i5 


45-34 


23-35 


45-24 


23-55 


45-l3 


23-75 


5i 


52 


46-33 


23 


61 


46 


23 


23 


81 


46 


12 


24 


01 


46 


02 


24 


21 


52 


53 


47-22 


24 


06 


47 


12 


24 


27 


47 


01 


24 


47 


46 


90 


24 


68 


53 


54 


48-u 


24 


52 


48 


01 


24 


73 


47 


90 


24 


9 3 


47 


79 


25 


14 


54 


55 


49-01 


24 


97 


48 


90 


25 


18 


48 


79 


25 


40 


48 


67 


25 


61 


55 


56 


49-90 


25 


42 


49 


78 


25 


64 


49 


67 


25 


86 


49 


56 


26 


07 


56 


5 7 


5o-79 


25 


88 


5o 


67 


26 


10 


5o 


56 


26 


32 


5o 


44 


26 


54 


5 7 


58 


5i-68 


26 


33 


5i 


56 


26 


56 


5i 


45 


26 


78 


5i 


33 


27 


01 


58 


5 9 


52-57 


26 


79 


52 


45 


27 


01 


52 


33 


27 


24 


52 


21 


27 


47 


5 9 


6o 


53-46 


27 


24 


53 


34 


27 


47 


53 


22 


27 


70 


53 


10 


27 


94 


60 


6i 


54-35 


27. 


$ 


54 


23 


27 


9 3 


54 


11 


28 


17 


53 


98 


28 


4o 


61 


62 


55-24 


28. 


55 


12 


28 


3 9 


54 


99 


28 


63 


54 


87 


28 


87 


62 


63 


5(5-13 


28. 


60 


56 


01 


28 


85 


55 


88 


29 


09 


55 


7 5 


29 


33 


63 


64 


57-02 


29. 


06 


56 


90 


29 


3o 


56 


77 


29 


5d 


56 


64 


29 


80 


64 


65 


57.92 


29. 


5i 


5 7 


79 


29 


76 


57 


66 


3o 


01 


57 


52 


3o 


26 


65 


66 


58- 81 


29. 


96 


58 


68 


3o 


22 


58 


54 


3o 


48 


58 


4i 


3o 


73 


66 


67 


59-70 


3o 


42 


5 9 


56 


3o 


68 


5 9 


43 


3o 


94 


5 9 


29 


3i 


20 


67 


68 


6o- 5o 


3o 


87 


60 


45 


3i 


14 


60 


32 


3i 


40 


60 


18 


3i 


66 


68 


69 


61-48 


3i 


33 


61 


34 


3i 


5 9 


61 


20 


3i 


86 


61 


06 


32 


i3 


69 


70 


62-37 


3i 


78 


62 


23 


32 


o5 


62 


09 


32 


32 


61 


9 5 


32 


5 9 


70 


7i 


63-26 


32 


23 


63 


12 


32 


5i 


62 


98 


32 


78 


62 


83 


33 


06 


7i 


72 


64-i5 


32 


69 


64 


01 


32 


97 


63 


86 


33 


25 


63 


72 


33 


52 


72 


73 


65-o4 


33 


14 


64 


90 


33 


42 


64 


75 


33 


71 


64 


60 


33 


99 


73 


74 


65- 9 3 


33 


60 


65 


79 


33 


88 


65 


64 


34 


17 


65 


49 


34 


46 


74 


75 


66-83 


34 


o5 


66 


68 


34 


34 


66 


53 


34 


63 


66 


37 


34 


92 


^ 


76 


67.72 


34 


5o 


67 


57 


34 


80 


67 


4i 


35 


09 


67 


26 


35 


3 9 


76 


77 


68-6i 


34 


96 


68 


45 


35 


26 


68 


3o 


35 


55 


68 


14 


35 


85 


77 


78 


69.50 


35 


41 


69 


34 


35 


7i 


69 


'9 


36 


02 


69 


o3 


36 


32 


78 


8 


70.39 


35 


87 


70 


23 


36 


17 


70 


07 


36 


48 


69 


9i 


36 


78 


I 9 


71-28 


36 


32 


7i 


12 


36 


63 


70 


96 


36 


94 


70 


80 


37 


25 


80 


81 


72-17 


36 


77 


72 


01 


37 


09 


7i 


85 


37 


40 


71 


68 


37 


71 


81 


82 


73-o6 


37 


23 


72 


90 


37 


55 


72 


73 


37 


86 


72 


5 7 


38 


18 


82 


83 


73.o5 


3 7 


68 


73 


79 


38 


00 


73 


62 


38 


33 


73 


45 


38 


65 


83 


84 


74-84 


38 


14 


74 


68 


38 


46 


74 


5i 


38 


79 


74 


■ 34 


b 


11 


84 


85 


75-74 


38 


5 9 


75 


5 7 


38 


92 


75 


4o 


3 9 


25 


75 


22 


39 


58 


85 


86 


76-63 


3 9 


04 


76 


46 


3 9 


38 


76 


28 


3 9 


7i 


76 


11 


40 


04 


86 


87 


77-52 


3 9 


5o 


77 


34 


39 


83 


77 


n 


40 


17 


76 


99 


40 


5i 


87 


88 


78-41 


39 


9 5 


78 


23 


40 


29 


78 


06 


40 


63 


77 


88 


40 


97 


88 


89. 


79 -3o 


4o 


4i 


79 


12 


4o 


75 


78 


2 4 


4i 


10 


78 


76 


41 


44 


89 


90 


80-19 


40 


86 


80 


01 


4i 


21 


79 


83 


4i 


56 


79 


65 


41 


9 1 


90 


9 1 


81-08 


4i 


3i 


80 


90 


4i 


67 


80 


72 


42 


02 


8o 


53 


42 


37 


9i 


92 


81.97 


4i 


•77 


81 


79 


42 


12 


81 


60 


42 


48 


81 


42 


42 


84 


92 


9 3 


82-86 


42 


■22 


82 


68 


42 


58 


82 


49 


42 


94 


82 


3o 


43 


3o 


93 


94 


83- 7 5 


42 


• 68 


83 


5 7 


43 


04 


83 


38 


43 


4o 


83 


19 


43 


77 


H 


9 5 


84-65 


43 


-i3 


84 


• 46 


43 


5o 


84 


27 


43 


87 


84 


07 


44 


23 


95 


96 


85-54 


43 


-58 


85 


• 35 


43 


96 


85 


i5 


44 


33 


84 


96 


44 


70 


96 


97 


86-43 


44 


.04 


86 


•23 


44 


4i 


86 


04 


44 


79 


85 


84 


45 


16 


9 Z 


9 8 


87.32 


44 


:S 


87 


■12 


44 


87 


86 


o3 


45 


2D 


86 


73 


45 


63 


98 


99 


88-21 


44 


88 


•01 


45 


33 


87 


81 


45 


7i 


87 


61 


46 


10 


99 


100 


89-10 


45.40 


88-90 


45.79 


88-70 


46-17 


88- 5o 


46-56 


100 


Distance. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




a 

5 


6 


3° 


62 


30 


62£° 


62i° 



142 






TRAVERSE TABLE. 




Table IV. 


g 

Si' 


28° 


28i° 


28|° 


28 


1° 


g 

a 


n 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


0-88 


0-47 


0-88 


0-47 


o-88 


0-48 


0-88 


o-48 


I 


2 


1 


77 





94 


1 


76 





9 5 


1 


76 





9 5 


1 


75 





96 


2 


3 


2 


65 


1 


4i 


2 


64 


1 


42 


2 


64 


I 


43 


2 


63 


1 


44 


3 


4 


3 


53 


1 


88 


3 


52 


1 


89 


3 


52 


I 


9 1 


3 


5i 


1 


92 


4 


5 


4 


4i 


2 


35 


4 


4o 


2 


37 


4 


39 


2 


39 


4 


38 


2 


4o 


5 


6 


5 


3o 


2 


82^ 


5 


29 


2 


84 


5 


27 


2 


86 


5 


26 


2 


89 


6 


2 


6- 


18 


3 


29 


6 


n 


3 


3i 


6 


i5 


3 


34 


6 


14 


3 


37 


7 


7- 


06 


3 


76 


7 


o5 


3 


79 


7 


o3 


3 


82 


7 


01 


3 


85 


8 


9 


7 


9 5 


4 


23 


7 


o3 


4 


26 


7 


9i 


4 


29 


7 


89 


4 


33 


9 


10 


8 


83 


4 


69 


8 


81 


4 


73 


8 


79 


4 


77 


8 


77 


4 


81 


10 


ii 


9- 


7i 


5 


16 


9 


69 


5 


21 


9 


67 


5 


25 


9 


64 


5 


29 


11 


12 


10- 


60 


5 


63 


10 


57 


5 


68 


10 


55 


5 


73 


10 


52 


5 


77 


12 


i3 


n< 


48 


6 


10 


11 


45 


6 


i5 


11 


42 


6 


20 


11 


40 


6 


25 


i3 


U 


12. 


36 


6 


57 


12 


33 


6 


63 


12 


3o 


6 


68 


12 


27 


6 


73 


14 


i5 


i3- 


24 


7 


04 


i3 


21 


7 


10 


i3 


18 


7 


16 


i3 


i5 


7 


21 


i5 


16 


i4- 


i3 


7 


5i 


14 


09 


7 


57 


14 


06 


7 


63 


14 


o3 


7 


70 


16 


17 


i5. 


01 


7 


98 


14 


98 


8 


o5 


14 


94 


8 


11 


14 


90 


8 


18 


17 


18 


i5- 


89 


8 


45 


i5 


86 


8 


52 


i5 


82 


8 


5 9 


i5 


78 


8 


-66 


18 


J 9 


16. 


7» 


8 


92 


16 


74 


8 


99 


16 


70 


9 


07 


16 


66 


9 


•14 


*9 


20 


m- 


66 


9 


3 9 


n 


62 


9 


47 


17 


58 


9 


54 


17 


53 


9 


•62 


20 


21 


18. 


54 


9 


86 


18 


5o 


9 


94 


18 


46 


10 


02 


18 


4i 


10 


• 10 


21 


22 


19 


42 


10 


33 


19 


38 


10 


4i 


19 


33 


10 


5o 


19 


29 


10 


58 


22 


23 


20 


3i 


10 


80 


20 


26 


10 


89 


20 


21 


10 


97 


20 


.16 


11 


.06 


23 


24 


21 


x 9 


11 


27 


21 


14 


11 


36 


21 


09 


11 


45 


21 


04 


11 


• 54 


24 


25 


22 


07 


11 


74 


22 


02 


11 


83 


21 


97 


11 


93 


21 


92 


12 


•02 


25 


26 


22 


t 


12 


21 


22 


90 


12 


3i 


22 


85 


12 


4i 


22 


79 


12 


•5i 


26 


27 


23 


12 


68 


23 


78 


12 


78 


23 


73 


12 


88 


23 


67 


12 


•99 


27 


28 


24 


72 


i3 


i5 


24 


66 


i3 


25 


24 


61 


i3 


36 


24 


55 


i3 


•47 


28 


29 


25 


61 


i3 


61 


25 


55 


i3 


73 


25 


49 


i3 


84 


25 


43 


i3 


9 5 


29 


3o 


26- 


49 


14 


08 


26 


43 


14 


20 


26 


36 


14 


3i 


26 


3o 


14 


43 


3o 


3i 


27 


37 


14 


55 


27 


3i 


14 


67 


• 27 


24 


14 


79 


27 


18 


14 


9i 


3i 


32 


28 


25 


i5 


02 


28 


J 9 


i5 


i5 


28 


12 


i5 


27 


28 


06 


i5 


39 


32 


33 


29 


14 


i5 


49 


29 


07 


i5 


62 


29 


00 


i5 


75 


28 


93 


i5 


87 


33 


34 


3o 


02 


i5 


96 


29 


9 5 


16 


09 


29 


88 


16 


22 


29 


81 


16 


35 


34 


35 


3o 


90 


16 


43 


3o 


83 


16 


5 7 


3o 


76 


16 


70 


3o 


69 


16 


-83 


35 


36 


3i 


79 


16 


90 


3i 


7i 


17 


04 


3i 


64 


17 


18 


3i 


56 


17 


■32 


36 


37 


32 


67 


17 


37 


32 


5 9 


n 


5i 


32 


52 


17 


65 


32 


44 


17 


■80 


3 l 


38 


33 


55 


17 


84 


33 


47 


17 


99 


33 


39 


18 


i3 


33 


32 


18 


28 


38 


3 9 


34 


43 


18 


3i 


34 


35 


18 


46 


34 


27 


18 


61 


34 


l 9 


18 


76 


3 9 


4o 


35 


32 


18 


78 


35 


24 


18 


9 3 


35 


i5 


19 


09 


35 


07 


*9 


24 


40 


41 


36 


20 


l 9 


25 


36 


12 


l 9 


4i 


36 


o3 


l 9 


56 


35 


o5 


l 9 


72 


4i 


42 


37 


08 


l 9 


72 


37 


00 


l 9 


88 


36 


9 1 


20 


04 


36 


82 


20 


20 


42 


43 


37 


97 


20 


*9 


37 


88 


20 


35 


37 


79 


20 


52 


37 


70 


20 


68 


43 


44 


38 


85 


20 


66 


38 


76 


20 


83 


38 


67 


20 


99 


38 


58 


21 


16 


44 


45 


3 9 


73 


21 


i3 


39 


64 


21 


3o 


39 


55 


21 


47 


39 


45 


21 


64 


45 


46 


40 


62 


21 


60 


40 


52 


21 


77 


40 


43 


21 


9 5 


40 


33 


22 


i3 


46 


47 


4i 


• 5o 


22 


07 


41 


4o 


22 


25 


4i 


3o 


22 


43 


4i 


21 


22 


61 


47 


48 


42 


• 38 


22 


53 


42 


28 


22 


72 


42 


18 


22 


90 


42 


08 


23 


09 


48 


49 


43 


• 26 


23 


•00 


43 


16 


23 


19 


43 


06 


23 


38 


42 


06 


23 


57 


49 


5o 


44. i5 


23-47 


44-04 


23-67 


43.94 


23-86 


43.84 


24-o5 


5o 




a 

s 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




a 

as 

02 

5 


6' 


2° 


61|° 


61i° 


61 


10 

4 



Table IV. 




TRAVERSE TABLE. 






143 


g 

So- 
ts 
3 
a 
? 


, 28° 


28i° 


28i° 


28|° 


m 

s 

CD 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


45- 03 


23- q4 


44-93 


24-14 


44-82 


24-34 


44-71 


24-53 


5i 


52 


45-91 


24 


4i 


45 


81 


24 


61 


45 


70 


24- 


81 


45- 


5 9 


25- 


01 


52 


53 


46-80 


24- 


88 


46 


69 


25- 


09 


46- 


58 


25- 


29 


46- 


47 


25- 


4 9 


53 


54 


47-68 


25- 


35 


47 


57 


20 


56 


47 


46 


25- 


77 


47- 


34 


25- 


97 


54 


55 


48-56 


25- 


82 


48 


45 


26 


o3 


48 


33 


26. 


24 


48- 


22 


26- 


45 


55 


56 


49-45 


26. 


29 


49 


33 


26 


5i 


49 


21 


26- 


72 


49. 


10 


26- 


94 


56 


57 


5o-33 


26- 


76 


5o 


21 


26 


98 


5o- 


09 


27. 


20 


49. 


97 


27- 


42 


57 


58 


5l-2I 


27. 


23 


5i. 


09 


27- 


45 


5o- 


97 


27. 


68 


5o 


85 


27. 


90 


58 


5 9 


52-09 


27- 


70 


5i- 


97 


27 


93 


5i- 


85 


28. 


i5 


5i 


73 


28 


38 


5 9 


6o 


52 -98 


28. 


17 


52- 


85 


28 


40 


52- 


73 


28. 


63 


52 


60 


28 


86 


60 


6i 


53-86 


28. 


64 


53- 


73 


28- 


87 


53- 


61 


29 


11 


53 


48 


29 


34 


61 


62 


54-74 


29. 


11 


54- 


62 


29. 


35 


54- 


49 


29. 


58 


54 


36 


29 


82 


62 


63 


55-63 


29. 


58 


55- 


5o 


29 


82 


55 


37 


3o 


06 


55 


23 


3o 


3o 


63 


64 


56-5i 


3o- 


o5 


56- 


38 


3o- 


29 


56 


24 


3o 


54 


56 


11 


3o 


78 


64 


65 


57-39 


3o- 


52 


5 7 . 


26 


3o- 


77 


57 


12 


3i 


02 


56 


99 


3i 


26 


65 


66 


58-27 


3o- 


99 


58- 


14 


3i- 


24 


58 


00 


3i 


49 


57 


86 


3i 


75 


66 


6 2 


59-16 


3i- 


45 


5 9 - 


02 


3i- 


7i 


58 


88 


3i 


97 


58 


74 


32 


23 


67 


68 


6o-o4 


3i- 


92 


5 9 - 


90 


32- 


*9 


5 9 


76 


32 


45 


59 


62 


32 


7 1 


68 


69 


60-92 


32- 


39 


60 • 


78 


32 


66 


60 


64 


32 


92 


60 


49 


33 


l 9 


69 


70 


61 • 81 


32- 


86 


6i- 


66 


33 


i3 


61 


52 


33 


40 


61 


37 


33 


67 


70 


7i 


62-69 


33- 


33 


62 


54 


33 


61 


62 


4o 


33 


88 


62 


25 


34 


i5 


7i 


72 


63-57 


33. 


80 


63 


42 


34 


08 


63 


27 


34 


36 


63 


12 


34 


63 


72 


73 


64-46 


34 


27 


64 


3o 


34 


55 


64 


i5 


34 


83 


64 


00 


35 


11 


73 


74 


65-34 


34 


74 


65 


*9 


35 


o3 


65 


o3 


35 


3i 


64 


88 


35 


5 9 


74 


7 5 


66-22 


35 


21 


66 


07 


35 


5o 


65 


9 1 


35 


79 


65 


75 


36 


07 


75 


76 


67-10 


35 


68 


66 


9 5 


35 


97 


66 


79 


36 


26 


66 


63 


36 


56 


76 


? 


67-09 


36 


i5 


67 


83 


36 


45 


67 


67 


36 


74 


67 


5i 


37 


04 


7 2 


68-87 


36 


62 


68 


7i 


36 


92 


68 


55 


37 


22 


68 


38 


37 


52 


78. 


79 


69.75 


37 


09 


69 


59 


37 


39 


69 


43 


37 


70 


69 


26 


38 


00 


I 9 


80 


70-64 


37 


56 


70 


47 


37 


87 


70 


3i 


38 


n 


70 


i4 


38 


48 


80 


81 


71-52 


38 


o3 


7 1 


35 


38 


34 


7 1 


18 


38 


65 


7i 


01 


38 


.96 


81 


82 


72-40 


38 


5o 


72 


23 


38 


81 


72 


06 


39 


i3 


7 1 


.89 


39 


■44 


82 


83 


73-28 


38 


97 


73 


11 


39 


29 


72 


2 4 


3 9 


60 


72 


•77 


3 9 


■ 92 


83 


84 


74-17 


39 


44 


73 


90 


39 


76 


73 


82 


40 


08 


73 


■ 64 


4o 


•40 


84 


85 


75-o5 


39 


OI 


74 


88 


4o 


23 


74 


70 


40 


• 56 


74 


•52 


4o 


• 88 


85 


86 


73-o3 


40 


37 


75 


76 


4o 


71 


75 


58 


4i 


04 


75 


.40 


4i 


• 36 


86 


87 


76-82 


40 


84 


76 


64 


4i 


.18 


76 


.46 


4i 


• 5i 


76 


-28 


4i 


• 85 


87 


88 


77.70 


4i 


3i 


77 


•52 


4i 


• 65 


77 


•34 


4i 


99 


77 


-i5 


42 


• 33 


88 


89 


78-58 


4i 


78 


78 


■40 


42 


-i3 


78 


•21 


42 


•47 


78 


■o3 


42 


•81 


89 


90 


79-47 


42 


25 


79 


■28 


42 


• 6o 


79 


09 


42 


■94 


78 


■91 


43 


•29 


90 


9i 


80-35 


42 


72 


80 


• 16 


43 


• 07 


79 


•97 


43 


•42 


79 


•78 


43 


•77 


9 1 


92 


8l- 23 


43 


• 19 


81 


■04 


43 


■ 55 


80 


85 


43 


• 90 


80 


• 66 


44 


•25 


92 


9 3 


82-11 


43 


• 66 


81 


'9 2 


44 


•02 


81 


•73 


44 


■ 38 


81 


•54 


44 


•73 


93 


94 


83-oo 


44 


•i3 


82 


• 80 


44 


•49 


82 


61 


44 


85 


82 


•4i 


45 


•21 


94 


9 5 


83-88 


44 


.60 


83 


• 68 


44 


•97 


83 


•49 


45 


■ 33 


83 


-29 


45 


.69 


9 5 


96 


84-76 


45 


•07 


84 


•5 7 


45 


•44 


84 


37 


45 


81 


84 


■17 


46 


■17 


96 


97 


85-65 


45 


•54 


85 


•45 


45 


•91 


85 


•25 


46 


28 


85 


• 04 


46 


66 


91 


98 


86-53 


46 


■01 


86 


■33 


46 


•39 


86 


•12 


46 


76 


85 


92 


47 


14 


98 


99 


87-41 


46 


-48 


87 


• 21 


46 


86 


87 


00 


47 


24 


86 


80 


47 


62 


99 


100 


88-29 


46-95 


88-09 


47-33 


87-88 


47-72 


87.67 


48-10 


100 


CD 
O 

a 

03 

a 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


0> 



c 

en 

Q 


6 


2° 


61 


!° 


61i° 


61 


i° 



144 






TRAVERSE TABLE. 




Table IV. 


g 

ft- 
p 

a 

JO 


2 


3° 


29i° 


29i° 


2S 


1° 


g 


? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


0-87 


0-48 


0-87 


0-49 


0-87 


0-49 


0.87 


o-5o 


I 


2 


I 


75 





97 


I 


74 


O.98 


I 


74 


0-98 


I 


•74 





•99 


2 


3 


2 


62 


1 


45 


2 


62 


1-47 


2 


61 


1.48 


2 


•6o 


1 


•49 


3 


4 


3 


5o 


1 


94 


3 


4 9 


1 -90 


3 


48 


1-97 


3 


•47 


1 


.98 


4 


5 


4 


37 


2 


42 


4 


36 


2-44 


4 


35 


2-46 


4 


•34 


2 


.48 


5 


6 


5 


25 


2 


91 


5 


23 


2-93 


5 


22 


2-95 


5 


•21 


2 


■98 


6 


2 


6 


12 


3 


39 


6 


11 


3-42 


6 


09 


3-45 


6 


■08 


3 


•47 


7 


7 


00 


3 


88 


6 


98 


3-91 


6 


96 


3- 9 4 


6 


•o5 


3 


•97 


8 


9 


7 


87 


4 


36 


7 


85 


4.40 


7 


83 


4-43 


7 


•01 


4 


•47 


9 


10 


8 


75 


4 


85 


8 


72 


4-8 9 


8 


70 


4-92 


8 


• 68 


4 


.96 


10 


ii 


9 


62 


5 


33 


9 


60 


5.37 


9 


57 


5.42 


9 


■ 55 


5 


•46 


11 


12 


10 


5o 


5 


82 


10 


47 


5-86 


10 


44 


5.91 


10 


•42 


5 


• 9 5 


12 


i3 


11 


37 


6 


3o 


11 


34 


6-35 


11 


3i 


6-4o 


11 


' 2 9 


6 


•45 


i3 


U 


12 


24 


6 


79 


12 


21 


6-84 


12 


18 


6-89 


12 


■16 


6 


• 9 5 


14 


i5 


i3 


12 


7 


27 


i3 


09 


7-33 


i3 


06 


7.39 


i3 


■ 02 


7 


•44 


i5 


16 


i3 


99 


7 


76 


i3 


96 


7.82 


i3 


o3 


7-88 


i3 


.89 


7 


•94 


16 


17 


14 


87 


8 


24 


14 


83 


8-3i 


14 


80 


8.37 


14 


.76 


8 


•44 


17 


18 


i5 


74 


8 


73 


i5 


70 


8-8o 


i5 


67 


8-86 


i5 


• 63 


8 


• 9 3 


18 


*9 


16 


62 


9 


21 


16 


58 


9-28 


16 


54 


9-36 


16 


• 5o 


9 


-43 


J 9 


20 


n 


49 


9 


70 


n 


45 


9-77 


17 


4i 


9-85 


17 


• 36 


9 


•92 


20 


21 


18 


37 


10 


18 


18 


32 


10-26 


18 


28 


10-34 


18 


•23 


10 


•42 


21 


22 


19 


24 


10 


67* 


19 


19 


10-75 


19 


i5 


10-83 


19 


• 10 


10 


.92 


22 


23 


20 


12 


11 


i5 


20 


07 


11-24 


20 


02 


u-33 


*9 


.97 


11 


•4i 


23 


24 


20 


99 


11 


64 


20 


94 


ii- 7 3 


20 


89 


11-82 


20 


• 84 


11 


.91 


24 


25 


21 


87 


12 


12 


21 


81 


12-22 


21 


76 


I2-3l 


21 


.70 


12 


•4i 


25 


26 


22 


74 


12 


60 


22 


68 


12-70 


22 


63 


12-80 


22 


•57 


12 


• 90 


26 


27 


23 


61 


i3 


09 


23 


56 


i3 • 19 


23 


5o 


i3-3o 


23 


•44 


i3 


■40 


27 


28 


24 


49 


i3 


57 


24 


43 


i3-68 


24 


37 


13.79 


24 


3i 


i3 


.89 


28 


29 


25 


36 


14 


06 


25 


3o 


14-17 


25 


24 


14-28 


25 


18 


14 


3 9 


29 


3o 


26 


24 


14 


54 


26 


17 


14-66 


26 


11 


14.77 


26 


o5 


14 


89 


3o 


3i 


27 


11 


i5 


o3 


27 


o5 


i5-i5 


26 


98 


i5-27 


26 


9 1 


i5 


38 


3i 


32 


27 


99 


i5 


5i 


27 


92 


i5-64 


27 


85 


i5- 7 6 


27 


78 


i5 


88 


32 


33 


28 


86 


16 


00 


28 


79 


16-12 


28 


72 


l6- 25 


28 


65 


16 


38 


33 


34 


29 


74 


16 


48 


29 


66 


16. 61 


29 


5 9 


16-74 


29 


52 


16 


87 


34 


35 


3o 


61 


16 


97 


3o 


54 


17. 10 


3o 


46 


17-23 


3o 


3q 


n 


37 


35 


36 


3i 


49 


H 


45 


3i 


4i 


I7-59 


3i 


33 


17.73 


3i 


26 


17 


86 


36 


37 


32 


36 


n 


94 


32 


28 


18-08 


32 


20 


18-22 


32 


12 


18 


36 


37 


38 


33 


24 


18 


42 


33 


i5 


i8-5 7 


33 


07 


l8-71 


32 


99 


18 


86 


38 


3 9 


34 


1 1 


18 


91 


34 


o3 


19-06 


33 


04 


I9-20 


33 


86 


l 9 


35 


39 


4o 


34 


98 


l 9 


3 9 


34 


90 


19-54 


34 


81 


I9-70 


34 


73 


*9 


85 


40 


4i 


35 


86 


*9 


88 


35 


77 


20- o3 


35 


68 


20-19 


35 


60 


20 


34 


41 


42 


36 


73 


20 


36 


36 


64 


20-52 


36 


55 


20-68 


36 


46 


20 


84 


42 


43 


37 


61 


20 


85 


37 


52 


21 -01 


37 


43 


21-17 


37 


33 


21 


34 


43 


44 


38 


48 


21 


33 


38 


39 


21 -5o 


38 


3o 


21-67 


38 


20 


21 


83 


44 


45 


3 9 


36 


21 


82 


39 


26 


21-99 


3 9 


n 


22-l6 


3 9 


07 


22 


33 


45 


46 


4o 


23 


22 


3o 


4o 


1-3 


22-48 


4o 


04 


22-65 


39 


94 


22 


83 


46 


47 


4i 


11 


22 


79 


41 


01 


22-97 


4o 


9 1 


23-i4 


40 


81 


23 


32 


47 


48 


4i 


98 


23 


27 


4i 


88 


23-45 


4i 


78 


23-63 


4i 


67 


23 


82 


48 


49 


42 


86 


23 


76 


42 


75 


23-94 


42 


65 


24-i3 


42 


54 


24. 


3i 


P 


5o 


43.73 


24-24 


43-62 


24-43 


43-52 


24-62 


43.41 


24-8.1 


5o 


e 

u 

ss 
a 

00 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


<D 

O 

C 

ca 


6 


L° 


60 


1° 


60 


1° 


60 


\° 



Table IV. 




TRAVERSE TABLE. 




145 


g 

Si* 

a 
a 
? 


29° 


29i° 


29£° 


29|° 


O 

3 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


44- 61 


24-73 


44 -5o 


24-92 


44-3 9 


25-11 


44-28 


25-3i 


5i 


52 


45-48 


25-21 


45 


•3 7 


26.41 


45-26 


25-6i 


45-i5 


25- 80 


52 


53 


46-35 


25-6o 


46 


•24 


25.90 


46- 13 


26-10 


46-01 


26- 3o 


53 


54 


47-23 


26.18 


47 


•11 


26-39 


47-oo 


26-59 


46-88 


26-80 


54 


55 


48-10 


26-66 


47 


•99 


26-87 


47-87 


27-08 


47-75 


27.29 


55 


56 


48-98 


27- 15 


48 


• 86 


27-36 


48.74 


27-58 


48-62 


27.79 


56 


5 7 


49-85 


27-63 


49 


•73 


27-85 


49-61 


28-07 


49.49 


28-28 


57 


58 


5o-73 


28-12 


5o 


• 6o 


28-34 


5o-48 


28-56 


5o-36 


28.78 


58 


59 


5i -6o 


28-60 


5i 


48 


28-83 


5i-35 


29-05 


5l-22 


29-28 


5 9 


6o 


52-48 


29-09 


52 


35 


29-32 


52-22 


29-55 


52-09 


29.77 


60 


6i 


53-35 


29.57 


53 


22 


29.81 


53-09 


3o-o4 


52^6 


30-27 


61 


62 


54-23 


3o-o6 


54 


09 


3o 


■29 


53.96 


3o-53 


53-83 


3o>77 


62 


63 


55' 10 


3o-54 


54 


97 


3o 


•78 


54-83 


3l-02 


54-70 


3i -26 


63 


64 


55- 9 8 


3i-o3 


55 


84 


3i 


•27 


55.70 


3i -52 


55-56 


3i- 7 6 


64 


65 


56-85 


3i-5i 


56 


7i 


3i 


.76 


56-57 


32-01 


56-43 


32-25 


65 


66 


57-72 


32-00 


57 


58 


32 


•25 


57-44 


32-5o 


57 -3o 


32-75 


66 


23 


58- 60 


32-48 


58 


46 


32 


•74 


58- 3i 


32-99 


58-17 


33-25 


67 


5 9 -47 


32-97 


5 9 


33 


33 


•23 


5 9 -i8 


33.48 


59-04 


33.74 


68 


6 9 


6o-35 


33-45 


60 


20 


33 


71 


60 -o5 


33.98 


59-9I 


34-24 


69 


70 


6l-22 


33- 9 4 


61 


07 


34 


■20 


60-92 


34-47 


60-77 


34-74 


70 


71 


62-10 


34-42 


61 


9 5 


34 


69 


6i-8o 


34-96 


61-64 


35-23 


7 1 


72 


62-97 


34-91 


62 


82 


35 


10 


62-67 


35-45 


62-5i 


35.73 


72 


73 


63-85 


35-3 9 


63 


69 


35 


67 


63-54 


35.95 


63-38 


36-22 


73 


74 


64-72 


35-88 


64 


56 


36 


16 


64-41 


36-44 


64-25 


36-72 


74 


75 


65- 60 


36-36 


65 


44 


36 


65 


65-28 


36 - 9 3 


65-n 


37-22 


75 


76 


66-47 


36-85 


66 


3i 


37 


14 


66-i5 


37-42 


65- 9 8 


37.71 


76 


7 2 


67-35 


3 7 -33 


67 


18 


37 


62 


67-02 


37-92 


66-85 


38-21 


77 


78 


68-22 


37-82 


68 


0.5 


38 


11 


67-89 


38-41 


67.72 


38.70 


78 


19 


69-09 


38- 3o 


68 


o3 


38 


60 


68-76 


38- 9 o 


68- 5 9 


39-20 


11 


80 


69.97 


38-78 


69 


80 


39 


09 


69. 63 


39.39 


69-46 


39.70 


81 


70-84 


39.27 


70 


67 


3 9 


58 


70- 5o 


3 9 .8o 


70.32 


40-19 


81 


82 


71-72 


39.75 


lp 


54 


4o 


07 


71.37 


4o-38 


71-19 


40 • 69 


82 


83 


72-5 9 


40-24 


72 


42 


4o 


56 


72-24 


40-87 


72-06 


41-19 


83 


84 


73.47 


40-72 


p 


29 


4i 


04 


73-11 


4i-36 


7 2 -93 


41-68 


84 


85 


74-34 


41-21 


74 


16 


4i 


53 


73.98 


41-86 


73-8o 


42-18 


85 


86 


75-22 


41-69 


7 5- 


o3 


42 


02 


74-85 


42-35 


74-67 


42-67 


86 


87 


76-09 


42-18 


75 


9i 


42 


5i 


75-72 


42-84 


75.53 


43-17 


87 


88 


76.97 


42-66 


76. 


78 


43 


00 


76-59 


43-33 


76.40 


43-6 7 


88 


89 


77-84 


43-i5 


77- 


65 


43 


4o 


77.46 


43-83 


77.27 


44-i6 


89 


90 


78.72 


43-63 


78- 


52 


43 


9« 


78.33 


44-32 


78-I4 


44-66 


90 


9 1 


79.59 


44-12 


79- 


4o 


44 


46 


79-20 


44-8i 


79.01 


45-i6 


9 1 I 


92 


80.46 


44- 60 


80 • 


27 


44 


9 5 


80-07 


45-3o 


79-87 


45-65 


9 2 


93 


81.34 


45-09 


81 • 


14 


45 


44 


80-94 


45- 80 


80-74 


46- 15 


9 3 


94 


82-21 


45-57 


82- 


01 


45 


93 


8i-8i 


46-29 


81.61 


46-64 


94 


9 5 


83-o 9 


46-06 


82- 


89 


46 


42 


82-68 


46-78 


82-48 


47-14 


95 


96 


83 -96 


46-54 


83- 


76 


46 


9i 


83-55 


47-27 


83-35 


47-64 


96 


97 


84-84 


47 -o3 


84- 


63 


47- 


4o 


84-42 


47-77 


84-22 


48-i3 


! 97 


98 


85. 7 i 


47-5i 


85- 


5o 


47- 


88 


85-2 9 


48-26 


85- 08 


48-63 


98 


99 


86-5 9 


48-00 


86- 


38 


48- 


37 


86-17 


48-75 


85- 9 5 


49-i3 


99 


100 


87.46 


48-48 


87-25 


48-86 


87-04 


49-24 


86.82 


49-62 


100 


« 


a 

OS 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


a" 


a 

at 

00 

Q 


61 





60f° 


60i° 


60£° 



146 






TRAVERSE TABLE. 




Table IV. 


g 

So' 

a 


30° 


30*° 


301° 


30 


1° 


D 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


0-87 


o-5o 


o-86 


o-5o 


o-86 


o-5i 


o-86 


o-5i 


I 


2 


1 


73 


1 


00 


1 


73 


I-OI 


1 


72 


1-02 


1 


72 


1 


02 


2 


3 


2 


60 


1 


5o 


2 


5 9 


i5i 


2 


58 


1-52 


2 


58 


1 


53 


3 


4 


3 


46 


2 


00 


3 


46 


2-02 


3 


45 


2-o3 


3 


44 


2 


o5 


4 


5 


4 


33 


2 


5o 


4 


32 


2-52 


4 


3i 


2-54 


4 


3o 


2 


56 


5 


6 


5 


20 


3 


00 


5 


18 


3-02 


5 


n 


3-o5 


5 


16 


3 


07 


6 


7 


6 


06 


3 


5o 


6 


o5 


3-53 


6 


o3 


3-55 


6 


02 


3 


58 


7 


8 


6 


9 3 


4 


00 


6 


9 1 


4-o3 


6 


89 


4-o6 


6 


88 


4 


09 


8 


9 


7 


79 


4 


5o 


7 


77 


4-53 


7 


73 


4-57 


7 


73 


4 


60 


9 


10 


8 


66 


5 


00 


8 


64 


5-o4 


8 


62 


5-o8 


8 


5 9 


5 


11 


10 


ii 


9 


53 


5 


5o 


9 


5o 


5.54 


9 


48 


5-58 


9 


45 


5 


62 


11 


12 


10 


3 9 


6 


00 


10 


37 


6-o5 


10 


34 


6-09 


10 


3i 


6 


U 


12 


i3 


11 


26 


6 


5o 


11 


23 


6-55 


11 


20 


6-6o 


11 


1.7 


6 


65 


i3 


14 


12- 


12 


7 


00 


12 


09 


7-o5 


12 


06 


7-n 


12 


o3 


7 


16 


14 


i5 


12 


29 


7 


5o 


12 


96 


7-56 


12 


92 


7-61 


12 


89 


7 


67 


i5 


16 


l3 


86 


8 


00 


i3 


82 


8-o6 


i3 


U 


8-12 


i3 


7 5 


8 


18 


16 


n 


U- 


72 


8 


5o 


14 


69 


8-56 


14 


8-63 


14 


61 


8 


69 


n 


18 


i5 


5o 


9 


00 


i5 


55 


9-07 


i5 


5i 


9-14 


i5 


47 


9 


20 


18 


*9 


16. 


45 


9 


5o 


16 


41 


9-5 7 


16 


37 


9.64 


16 


33 


9 


7i 


J 9 


20 


17' 


32 


10 


00 


n 


28 


10-08 


17 


23 


io-i5 


17 


19 


10 


23 


20 


21 


18 


19 


10 


5o 


18 


14 


io-58 


18 


09 


io-66 


18 


o5 


10 


74 


21 


22 


*9 


o5 


11 


00 


19 


00 


11-08 


18 


96 


11-17 


18 


9 1 


11 


25 


22 


23 


19 


92 


11 


5o 


'9 


87 


11-59 


19 


82 


11-67 


19 


77 


11 


76 


23 


24 


20 


78 


12 


00 


20 


73 


12-09 


20 


68 


12-18 


20 


63 


12 


27 


24 


25 


21 


65 


12 


5o 


21 


60 


12-59 


21 


54 


12-69 


21 


49 


12 


78 


25 


26 


22 


52 


i3 


00 


22 


46 


i3-io 


22 


4o 


l3-20 


22 


34 


i3 


29 


26 


27 


23 


38 


i3 


5o 


23 


32 


i3-6o 


23 


26 


13-70 


23 


20 


i3 


•80 


27 


28 


24- 


25 


14 


00 


24 


19 


14-n 


24 


i3 


14-21 


24 


06 


14 


32 


28 


29 


25 


11 


14 


5o 


25 


o5 


i4-6i 


24 


99 


14-72 


24 


92 


14 


83 


29 


3o 


25 


98 


i5 


00 


25 


92 


i5-ii 


25 


85 


15-23 


25 


78 


i5 


34 


3o 


3i 


26- 


85 


i5 


5o 


26 


78 


i5-62 


26 


7i 


15-73 


26 


64 


i5 


85 


3i 


32 


27 


7i 


16 


00 


27 


64 


16-12 


27 


57 


16-24 


27 


5o 


16 


36 


32 


33 


28 


58 


16 


5o 


28 


5i 


16-62 


28 


43 


16-75 


28 


36 


16 


87 


33 


34 


29. 


44 


17 


00 


29 


37 


i 7 -i3 


29 


3o 


17-26 


29 


22 


17 


38 


34 


35 


3o 


3i 


1.7 


5o 


3o 


23 


17-63 


3o 


16 


17-76 


3o 


08 


n 


90 


35 


36 


3i 


18 


18 


00 


3i 


10 


18-14 


3i 


02 


18-27 


3o 


Q4 


18 


41 


36 


37 


32 


04 


18 


5o 


3i 


96 


18-64 


3* 


88 


18.78 


3i 


00 


18 


92 


37 


38 


32 


91 


*9 


00 


32 


83 


19-14 


32 


74 


19-29 


32 


66 


*9 


43 


38 


3o 


33 


77 


*9 


5o 


33 


69 


ig-65 


33 


60 


19.79 


33 


52 


x 9 


94 


3 9 


4o 


34 


64 


20 


00 


34 


55 


20-l5 


34 


47 


20-30 


34 


38 


20 


45 


40 


4i 


35 


5i 


20 


5o 


35 


42 


20-65 


35 


33 


20-8l 


35 


24 


20 


96 


41 


42 


36 


37 


21 


00 


36 


28 


2I-l6 


36 


*9 


21-32 


36 


10 


.21 


47 


42 


43 


37 


24 


21 


5o 


37 


14 


21-66 


37 


o5 


21 -82 


36 


9 5 


21 


99 


43 


44 


38 


11 


22 


00 


38 


01 


22-17 


37 


9 1 


22-33 


37 


81 


22 


5o 


44 


45 


38 


97 


22 


5o 


38 


87 


22-67 


38 


77 


22-84 


38 


67 


23 


01 


45 


46 


39 


84 


23 


00 


39 


74 


23-17 


39 


63 


23-35 


3 9 


53 


23 


52 


46 


47 


4o 


70 


23 


5o 


4o 


60 


23-68 


4o 


5o 


23-85 


40 


3 9 


24 


o3 


47 


48 


4i 


5 7 


24 


00 


4i 


46 


24- 18 


4i 


36 


24-36 


4i 


25 


24 


54 


48 


4 9 


42 


■44 


24 


5o 


42 


33 


24-68 


42 


22 


24-87 


42 


11 


25 


o5 


49 


5o 


43 -3o 


25-00 


43-19 


25-19 


43-o8 


25-38 


42-97 


25-56 


5o 


£ 

o 

e 
a 

m 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat 




I 


6 


)° 


59|° 


59 


h° 


59 


1° 


' 



Table IV. 


TRAVERSE TABLE. 




1 

147 


? 


30° 


30i° 


30£° 


30f° 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


44-17 


25-5o 


44- 06 


25- 6g 


43.94 


25-88 


43-83 


26-08 


5i 


52 


45 


o3 


26 


00 


44 


92 


26 


20 


44 


80 


26-39 


44- 


69 


26-59 


52 


53 


45 


90 


26 


5o 


45. 


78 


26 


70 


45 


67 


26-90 


45 


55 


27-10 


53 


54 


46 


77 


27 


00 


46 


65 


27 


20 


46 


53 


27-41 


46 


4i 


27-61 


54 


55 


47 


63 


27. 


5o 


47- 


5i 


27 


7i 


47 


39 


27-91 


47 


27 


28-12 


55 


56 


48 


5o 


28 


00 


48 


37 


28 


21 


48 


25 


28-42 


48- 


i3 


28-63 


56 


57 


49 


36 


28 


5o 


49 


24 


28 


72 


49 


11 


28- 9 3 


48 


99 


29-14 


5 7 


•58 


5o 


23 


29 


00 


5o 


10 


29 


22 


49 


97 


29-44 


49 


85 


29-65 


58 


5 9 


5i 


10 


29 


5o 


5o 


97 


29 


72 


5o 


84 


29-94 


5o 


70 


3o-i7 


59 


6o 


5i 


96 


3o- 


00 


5i 


83 


3o 


23 


5i 


70 


3o-45 


5i 


56 


3o-68 


60 


6i 


52 


83 


3o 


5o 


52 


69 


3o 


73 


52 


56 


30-96 


52 


42 


3i • 19 


61 


62 


53- 


69 


3i 


00 


53 


56 


3i 


23 


53 


42 


3i-47 


53 


28 


3i -70 


62 


63 


54 


56 


3i 


5o 


54 


42 


3i 


74 


54 


28 


3 1 -97 


54 


14 


32-21 


63 


64 


55 


43 


32- 


00 


55 


29 


32 


24 


55 


U 


32-48 


55 


00 


32-72 


64 


65 


56 


29 


32 


Do 


56 


i5 


3-2 


75 


56 


01 


33 -Do 


55 


86 


33-23 


65 


66 


5 7 


16 


33 


00 


5 7 


01 


33 


25 


56 


87 


56 


72 


33-75 


66 


67 


58 


02 


33 


5o 


5 7 


88 


33 


75 


57 


73 


34-oi 


5 7 


58 


34-26 


67 


68 


58 


89 


34 


00 


58 


74 


34 


26 


58 


5o 


34-5i 


58 


44 


34-77 


68 


69 


5 9 


76 


34 


5o 


5 9 


60 


34 


76 


5 9 


45 


35-02 


5 9 


3o 


35-28 


69 


70 


60 


62 


35 


00 


60 


47 


35 


26 


60 


3i 


35-53 


60 


16 


35.79 


70 


7i 


61 


49 


35 


5o 


61 


33 


35 


77 


61 


18 


36- 04 


61 


02 


36- 3o 


7i 


72 


62 


35 


36 


00 


62 


20 


36 


27 


62 


04 


36-54 


61 


88 


36-8i 


72 


73 


63 


22 


36 


5o 


63 


06 


36 


78 


62 


90 


37-o5 


62 


74 


37.32 


73 


74 


64 


09 


37 


00 


63 


92 


37 


28 


63 


76 


37-56 


63 


60 


37.84 


74 


7 5 


64 


9 5 


37 


5o 


64 


79 


37 


78 


64 


•62 


38-07 


64 


46 


38-35 


7 5 


76 


65 


82 


38 


00 


65 


65 


38 


29 


65 


48 


38-57 


65 


3i 


38-86 


76 


8 


66 


68 


38 


5o 


66 


52 


38 


79 


66 


35 


3 9 -o8 


66 


'7 


39-37 


77 


67 


55 


39 


00 


67 


38 


39 


29 


67 


21 


39.59 


i 1 


o3 


3 9 -88 


78 


79 


68 


42 


39 


5o 


68 


24 


39 


80 


68 


07 


4o-io 


67 


89 


40-39 


I 9 


80 


69 


28 


4o 


00 


69 


11 


4o 


3o 


68 


93 


40-60 


68 


76 


40-90 


80 


81 


70 


i5 


4o 


5o 


69 


97 


4o 


81 


69 


79 


4i-ii 


69 


61 


4i-4i 


81 


82 


7 1 


01 


4i 


00 


70 


83 


4i 


3i 


70 


65 


41-62 


70 


47 


41-93 


82 


83 


7i 


88 


4i 


5o 


7"i 


70 


4i 


81 


7i 


52 


42-i3 


7i 


33 


42-44 


83 


84 


72 


75 


42 


00 


72 


56 


42 


32 


72 


38 


42-63 


72 


T 9 


42-90 


84 


85 


73 


61 


42 


5o 


73 


43 


42 


82 


73 


24 


43-14 


73 


o5 


43-46 


85 


86 


74 


48 


43 


00 


74 


29 


43 


32 


74 


10 


43-65 


73 


■91 


43-97 


86 


S l 


75 


34 


43 


5o 


75 


i5 


43 


83 


74 


• 96 


44- 16 


74 


77 


44-48 


87 


88 


76 


21 


44 


00 


76 


02 


44 


33 


7 5 


■82 


44-66 


7 5 


63 


44-99 


88 


89 


77 


08 


44 


5o 


76 


88 


44 


84 


76 


• 68 


45-H 


76 


.40 


45-5i 


89 


90 


77 


94 


45 


00 


77 


75 


45 


34 


77 


■ 55 


45-68 


77 


•35 


46-02 


90 


9 1 


78 


81 


45 


5o 


78 


61 


45 


• 84 


78 


•4i 


46-19 


78 


•21 


46-53 


9 1 


92 


79 


67 


46 


00 


79 


47 


46 


•35 


79 


•27 


46-69 


79 


07 


47-04 


9? 


9 3 


80 


54 


46 


5o 


80 


34 


46 


85 


80 


•i3 


47-20 


79 


.92 


47-55 


93 


94 


81 


41 


47 


00 


81 


20 


47 


35 


80 


•99 


47-71 


80 


78 


48-06 


94 


9 5 


82 


27 


47 


• 5o 


82 


06 


47 


86 


81 


•85 


48-22 


81 


64 


48-5 7 


9 D 


96 


83 


•14 


48 


00 


82 


93 


48 


• 36 


82 


.72 


48-72 


82 


5o 


49-08 


96 


97 


84 


• 00 


48 


•5o 


83 


•79 


48 


•87 


83 


■ 58 


49-23 


83 


36 


49 • 60 


9 Z 


98 


84 


.87 


49 


• 00 


84 


66 


49 


•37 


84 


•44 


49-74 


84 


22 


5o-n 


98 


99 


85 


•74 


49 


• 5o 


85 


•52 


49 


•87 


85 


• 3o 


5o-25 


85 


08 


5o-62 


99 


100 


86-60 


5o-oo 


86-38 


5o-38 


86-16 


5o>75 


85-94 


5i-i3 


100 


6 


a 

IS 
aq 

a 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


c 

RS 
03 

s 


60° 


59|° 


59 


i° 


59i° 






















148 






TRAVERSE TABLE. 


Table IV. 


9 

55' 



S3 

n 
eg 


31° 


31i° 


31£° 


31|° 


i 

GO 

p» 

3 
O 
p 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


o-86 


o-5l 


o-85 


a-52 


0-85 


0-52 


o-85 


o-53 


I 


2 


1 


7i 


I 


o3 


1 


7i 


1 


04 


1 


71 


I- 04 


1 


70 


1 


o5 


2 


3 


2 


57 


I 


55 


, 2 


56 


1 


56 


2 


56 


1-57 


2 


55 


1 


58 


3 


4 


3 


43 


2 


06 


3 


42 


2 


08 


3 


41 


2-09 


3 


40 


2 


• 10 


4 


5 


4 


29 


2 


58 


i 4 


27 


2 


5 9 


4 


26 


2-6l 


4 


25 


2 


• 63 


5 


6 


5 


14 


3 


09 


5 


i3 


3 


11 


5 


12 


3-i3 


5 


10 


3 


.16 


6 


J 


6 


00 


3 


61 


5 


98 


3 


63 


5 


97 


3-66 


5 


•o5 


3 


• 68 


I 


6 


86 


4 


12 


6 


84 


4 


i5 


6 


82 


4-i8 


6 


•00 


4 


• 21 


9 


7 


7i 


4 


64 


7 


I 


4 


67 


7 


67 


4-70 


7 


65 


4 


.74 


9 


IO 


8 


57 


5 


i5 


| » 


5 


*9 


8 


53 


5-22 


8 


5o 


5 


-26 


10 


ii 


9 


43 


5 


67 


! 9 


4o 


5 


7i 


9 


38 


5-75 


9 


35 


5 


'79 


11 


12 


10 


29 


6 


18 


10 


26 


6 


23 


10 


23 


6 


27 


10 


20 


6 


• 3i 


12 


i3 


11 


14 


6 


70 


n 


11 


6 


74 


11 


08 


6 


79 


11 


o5 


6 


-84 


i3 


U 


12 


00 


7 


21 


1 11 


9J 


7 


26 


11 


94 


7 


3i 


11 


90 


7 


•3 7 


14 


i5 


12 


86 


7 


73 


12 


82 


7 


78 


12 


79 


7 


84 


12 


76 


7 


.89 


i5 


16 


i3 


7 1 


8 


24 


i3 


68 


8 


3o 


i3 


64 


8 


36 


i3 


•61 


8 


•42 


16 


\l 


14 


57 


8 


76 


14 


53 


8 


82 


14 


49 


8 


88 


14 


-46 


8 


- 9 5 


17 


i5 


43 


9 


27 


i5 


3 9 


9 


34 


i5 


35 


9 


4o 


i5 


-3i 


9 


•47 


18 


*9 


16 


29 


9 


79 


16 


24 


9 


86 


16 


20 


9 


93 


16 


■ 16 


10 


• 00 


19 


20 


17 


14 


10 


3o 


*7 


10 


10 


38 


17 


o5 


10 


45 


17 


•01 


10 


-52 


20 


21 


18 


00 


10 


82 


:*7 


9 5 


10 


89 


17 


91 


10 


97 


! 17 


• 86 


11 


-o5 


21 


22 


18 


86 


11 


33 


18 


81 


11 


41 


18 


76 


11 


49 


18 


•71 


11 


-58 


22 


23 


1 9 


7i 


11 


85 


19 


66 


11 


9 3 


19 


61 


12 


02 


! 9 


-56 


12 


• 10 


23 


24 


20 


57 


12 


36 


20 


52 


12 


45 


20 


46 


12 


54 


20 


•4i 


12 


• 63 


24 


25 


21 


43 


12 


88 


21 


37 


12 


97 


21 


32 


i3 


06 


21 


• 26 


i3 


.16 


25 


26 


22 


29 


i3 


39 


22 


23 


i3 


49 


22 


17 


i3 


58 


; 22 


•11 


i3 


•68 


26 


27 


23« 


14 


i3 


9 1 


23 


08 


14 


01 


23 


02 


14 


11 


22 


.96 


14 


•21 


27 


28 


24 


00 


14 


42 


23 


94 


14 


53 


23 


87 


14 


63 


23 


81 


14 


•73 


28 


29 


24 


86 


14 


94 


24 


79 


i5 


04 


24 


7 3 


i5 


i5 


24 


66 


i5 


•26 


29 


36 


25 


71 


i5 


45 


25 


65 


i5 


56 


25 


58 


i5 


67 


25 


5i 


i5 


•79 


3o 


3i 


26 


57 


i5 


97 


26 


5o 


16 


08 


26 


43 


16 


20 


26 


36 


16 


•3i 


3i 


32 


27 


43 


16 


48 


27 


36 


16 


60 


27 


28 


16 


72 


27 


21 


16 


.84 


32 


33 


28 


29 


n 


00 


28 


21 


n 


12 


28 


14 


17 


24 


28 


06 


17 


• 3 7 


33 


34 


29 


14 


H 


5i 


29 


°7 


n 


64 


28 


§9 


n 


76 


28 


9i 


17 


.89 


34 


35 


3o 


00 


18 


o3 


29 


92 


18 


16 


29 


84 


18 


29 


29 


76 


18 


•42 


35 


36 


3o 


86 


18 


54 


3o 


78 


18 


68 


3o 


70 


18 


81 


3o 


61 


18 


.94 


36 


\l 


3i 


72 


19 


06 


3i 


63 


*9 


*9 


3i 


55 


*9 


33 


3i 


46 


*9 


•47 


3 7 


38 


32 


57 


*9 


57 


32 


49 


J 9 


7i 


32 


4o 


x 9 


85 


32 


3i 


20 


00 


38 


3 9 


33 


43 


20 


09 


33 


34 


20 


23 


33 


25 


20 


38 


33 


16 


20 


•52 


3 9 


4o 


34 


29 


20 


60 


34 


20 


20 


75 


34 


11 


20 


90 


34 


01 


21 


•o5 


40 


4i 


35 


14 


21 


12 


35 


o5 


21 


27 


34 


96 


21 


42 


34 


86 


21 


57. 


4i 


42 


36 


00 


21 


63 


35 


9 1 


21 


79 


35 


81 


21 


94 


35 


71 


22 


10 


42 


43 


36 


86 


22 


i5 


36 


76 


22 


3i 


36 


66 


22 


47 


36 


57 


22 


63 


43 


44 


37 


72 


22 


66 


37 


62 


22 


83 


37 


52 


22 


99 


37 


42 


23 


i5 


44 


45 


38 


57 


23 


18 


38 


47 


23 


34 


38 


37 


23 


Dl 


38 


27 


23 


68 


45 


46 


3 9 


43 


23 


69 


3 9 


33 


23 


86 


3 9 


22 


24 


o3 


3 9 


12 


24 


21 


46 


% 


40 


29 


24 


21 


4o 


18 


24 


38 


4o 


07 


24 


56 


3 9 


97 


24 


73 


47 


41 


14 


24 


72 


4i 


04 


24 


90 


4o 


93 


25 


08 


4o 


82 


25 


26 


48 


49 


42 


00 


25 


24 


4i 


8g 


25 


42 


4i 


78 


25 


60 


4i 


67 


25 


78 


49 


5o 


42-86 


25-75 


42-76 


25-94 


42-63 


26-12 


42-52 


26- 3 1 


5o 





a 

in 

Q 


Dep. 


Lat. 


Dep, 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


cd 

c 

on 

Q 


5« 


J° 


58 


1° 


58 


i° 


58*° 









• 














I 

i 


Table IV. 




TRAVERSE TABLE. 




149 




b 

sr 

3 
a 
5 


3 


1° 


31i° 


31£° 


31|° 


g 

a 

a 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




5i 


43.72 


26-27 


43.6o 


26-46 


43-48 


26-65 


43.37 


26-84 


5i 




52 


44 


•5 7 


26 


.78 


44-46 


26 


.98 


44-34 


27 


•17 


44 


•22 


27-36 


52 




53 


45 


•43 


27 


■ 3o 


45-3i 


27 


•49 


45-19 


27 


.69 


45 


•07 


27-89 


53 


. 


54 


46 


.29 


27 


.81 


46-17 


28 


•01 


46-04 


28 


•21 


45 


•92 


28-42 


54 




55 


47 


■14 


28 


• 33 


47-02 


28 


■53 


46-90 


28 


•74 


46 


■77 


28-94 


55 




56 


48 


•00 


28 


84 


.47-88 


29 


•o5 


47-75 


29 


•26 


47 


•62 


29.47 


56 




57 


48 


86 


29 


36 


48- 7 3 


29 


.57 


48-6o 


29 


.78 


48 


•47 


29.99 


57 




58 


49 


72 


29 


87 


49-58 


3o 


• 09 


49.45 


3o 


• 3o 


49 


•32 


3o-52 


58 




5 9 


5o 


57 


3o 


39 


5o-44 


3o 


•6i 


5o-3i 


3o 


• 83 


5o 


•H 


3i-o5 


59 




6o 


5i 


43 


3o 


90 


5i-29 


3i 


•i3 


5i-i6 


3i 


• 35 


5i 


• 02 


3r-5 7 


60 




6i 


52 


29 


3i 


42 


52-i5 


3i 


65 


52-01 


3i 


.87 


5i 


.87 


32-10 


61 




62 


53 


14 


3i 


93 


53-00 


32 


.16 


52-86 


32 


• 3 9 


52 


.72 


32-63 


62 




63 


54 


00 


32 


45 


53-86 


32 


68 


53.72 


32 


• 92 


53 


■57 


33- 15 


63 




64 


54 


86 


32 


96 


54-71 


33 


20 


54-57 


33 


•44 


54 


■42 


33-68 


64 




65 


55 


72 


33 


48 


55-57 


33 


72 


55-42 


33 


.96 


55 


27 


34-20 


65 




66 


56 


57 


33 


99 


56-42 


34 


24 


56-27 


34 


-48 


56 


12 


34-73 


66 




67 


57 


43 


34 


5i 


57.28 


34 


76 


57-i3 


35 


01 


56 


98 


35-26 


67 , 




68 


58 


29 


35 


02 


58-i3 


35 


28 


57.98 


35 


53 


57 


82 


35.78 


68 




69 


5 9 


14 


35 


54 


58.99 


35 


80 


58-83 


36 


o5 


58 


67 


36-3i 


69 




70 


60 


00 


36 


o5 


59-84 


36 


3i 


5 9 -68 


36 


57 


5 9 


52 


36-83 


70 




7i 


60 


86 


36 


57 


60.70 


36 


83 


60 -54 


37 


10 


60 


37 


37-36 


7i 




72 


61 


72 


37 


08 


6i.55 


37 


35 


61-39 


37 


62 


61 


23 


37.89 


72 




73 


62 


57 


37 


60 


62-41 


37 


87 


62-24 


38 


14 


62 


08 


38-41 


73 




74 


63 


43 


38 


11 


63-26 


38 


39 


63-10 


38 


66 


62 


93 


38-94 


74 




t 


64 


29 


38 


63 


64-12 


38 


9 1 


63- §5 


39 


19 


63 


78 


39-47 


75 




76 


65 


14 


39 


U 


64-97 


39 


43 


64-80 


3 9 


7i 


64 


63 


39-99 


76 




77 


66 


00 


3 9 


66 


65-83 


39 


9 5 


65-65 


4o 


23 


65 


48 


4o-52 


]l 




78 


66 


86 


4o 


n 


66-68 


4o 


46 


66-5i 


4o 


75 


66 


33 


41-04 




79 


67- 


72 


4o 


69 


67-54 


4o 


98 


67 -36 


4i 


28 


67 


18 


4i-57 


11 




80 


68- 


57 


4i 


20 


68- 3 9 


4i 


5o 


68-21 


4i 


80 


68 


o3 


42-10 




81 


69 


43 


4i 


72 


69-25 


42 


02 


69-06 


42 


32 


68 


88 


42-62 


81 




82 


70 


29 


42 


23 


70-10 


42 


54 


69.92 


42 


84 


69 


73 


43-i5 


82 




83 


7i 


14 


42 


75 


70-96 


43 


06 


70-77 


43 


37 


70 


58 


43-68 


83 




84 


72 


00 


43 


26 


71-81 


43 


58 


71-62 


43 


89 


7i 


43 


44-20 


84 




85 


72 


86 


43 


78 


72-67 


44 


10 


72-47 


44 


41 


72 


28 


44-73 


85 




86 


7 3. 


72 


44 


29 


73.52 


44 


61 


73-33 


44 


93 


73 


1 3 


45-25 


86 




87 


74 


5 7 


44 


81 


74-38 


45 


i3 


74-18 


45 


46 


73 


98 


45.78 


87 




88 


75 


43 


45 


32 


75-23 


45 


65 


75-o3 


45 


98 


74 


83 


46-3i 


88 




89 


76. 


29 


45 


84 


76-09 


46 


n 


75.88 


46 


5o 


75 


68 


46-83 


89 




90 


77 


i5 


46 


35 


76-94 


46 


69 


76-74 


47 


02 


76 


53 


47-36 


90 




9i 


78 


00 


46 


87 


77- 80 


47 


21 


77-59 


47 


55 


77 


38 


47-89 


9* 




92 


78 


86 


47 


38 


78-65 


47 


73 


78-44 


48 


07 


78 


23 


48.41 


92 




9 3 


79 


72 


47 


90 


79-5i 


48 


25 


79. 3o 


48 


5 9 


79 


08 


48-94 


9 3 




94 


80 


57 


48 


4i 


80 -36 


48 


76 


8o-i5 


49 


11 


79 


93 


49-47 


94 




9 5 


81 


43 


48 


93 


8l-22 


49 


28 


81 -00 


49 


64 


80 


n 


49-99 


9 5 




96 


82 


29 


49 


44 


82-07 


4 9 - 


80 


8i- 85 


5o 


16 


8i- 


5o-52 


96 




97 


83 


i5 


49 


96 


82- 9 3 


5o- 


32 


82-71 


5o 


68 


82- 


48 


5i-o4 


97 




98 


84 


00 


5o 


47 


83-78 


5o- 


84 


83-56 


5i 


20 


83- 


33 


5i • 57 


98 




99 


84 


86 


5o 


99 


84-64 


5i- 


36 


84-41 


5i- 


73 


84. 


18 


52-IO 


99 




100 


83.72 


5i -5o 


85-49 


5i-88 


85-26 


52-25 


85-04 


52-62 


100 




£ 


a 
S 
K 

s 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 





a 

m 




5S 


>° 


58 


1° 


58 


h° 


58i° 



150 






TRAVERSE TABLE. 


• 


Table IV. 




d 

3 

<s 

? 


32° 


324° 


32 


i° 


32 


1° 


d 

n 


1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




I 


0-85 


0-53 


0-85 


o-53 


0-84 


o-54 


0-84 


o-54 


I 




2 


I 


70 


I 


06 


1 


69 


1 


07 


1 


69 


1 


07 


1 


68 


1 


08 


2 




3 


2 


54 


I 


5 9 


2 


54 


1 


60 


2 


53 


1 


61 


2 


52 


1 


62 


3 




4 


3 


3 9 


2 


12 


3 


38. 


2 


i3 


3 


37 


2 


i5 


3 


36 


2 


16 


4 


- 


5 


4 


24 


2 


65 


4 


23 


2 


67 


4 


22 


2 


69 


4 


21 


2 


70 


5 


: 


6 


5 


09 


3 


18 


5 


07 


3 


20 


5 


06 


3 


22 


5 


o5 


3 


•25 


6 




I 


5 


94 


3 


7i 


5 


92 


3 


74 


5 


90 


3 


76 


5 


89 


3 


•79 


7 


' 


6 


78 


4 


24 


6 


77 


4 


27 


6 


7 D 


4 


3o 


6 


73 


4 


-33 


8 




9 


7 


63 


4 


77 


7 


61 


4 


80 


7 


5 9 


4 


84 


7 


57 


4 


•87 


9 


| 


10 


8 


48 


5 


3o 


8 


46 


5 


34 


8 


43 


5 


37 


8 


41 


5 


•4i 


10 


; 


ii 


9 


33 


5 


83 


9 


3o 


5 


87 


9 


28 


5 


9 1 


9 


25 


5 


■ 9 5 


11 




12 


10 


18 


6 


36 


10 


i5 


6 


40 


10 


12 


6 


45 


10 


°2 


6 


•49 


12 


' 


i3 


ii 


02 


6 


89 


10 


§9 


6 


94 


10 


96 


6 


98 


10 


9 3 


7 


• o3 


i3 


; 


i4 


ii 


87 


7 


42 


11 


84 


7 


47 


11 


8l 


7 


52 


11 


77 


7 


-5 7 


14 




i5 


12 


72 


7 


9 5 


12 


69 


8 


00 


12 


65 


8 


06 


12 


62 


8 


• 11 


i5 


[ 


16 


i3 


5 7 


8 


48 


i3 


53 


8 


54 


i3 


49 


8 


60 


i3 


46 


8 


• 66 


16 




1.7 


i4 


42 


9 


01 


14 


38 


9 


07 


14 


34 


9 


i3 


14 


3o 


9 


• 20 


n 




18 


i5 


26 


9 


54 


i5 


22 


9 


61 


i5 


18 


9 


67 


i5 


14 


9 


•74 


18 


j 


'9 


16 


11 


10 


07 


16 


07 


10 


14 


16 


02 


10 


21 


i5 


98 


10 


•28 


*9 




20 


16 


9 6 


10 


60 


16 


9i 


10 


67 


16 


87 


10 


75 


16 


82 


10 


-82 


20 


■ 


21 


n 


81 


11 


i3 


17 


76 


11 


21 


n 


7i 


11 


28 


17 


66 


11 


•36 


21 




22 


18 


66 


11 


66 


18 


61 


11 


74 


18 


55 


11 


82 


18 


5o 


11 


• 90 


22 


| 


23 


19 


5i 


12 


19 


19 


45 


12 


27 


J 9 


4o 


12 


36 


»9 


34 


12 


•44 


23 




24 


20 


35 


12 


72 


20 


3o 


12 


81 


20 


24 


12 


90 


20 


18 


12 


•98 


24 




25 


21 


20 


i3 


25 


21 


14 


i3 


34 


21 


08 


i3 


43 


21 


o3 


i3 


-52 


25 




26 


22 


o5 


i3 


78 


21 


2 9 


i3 


87 


21 


93 


i3 


97 


21 


87 


14 


-07 


26 




27 


22 


90 


14 


3i 


22 


83 


14 


41 


22 


77 


14 


5i 


22 


7i 


14 


•61 


27 




28 


23 


75 


14 


84 


23 


68 


14 


94 


23 


61 


i5 


04 


23 


55 


i5 


•i5 


28 


1 


29 


24 


5 9 


1 5 


37 


24 


53 


i5 


47 


24 


46 


i5 


58 


24 


39 


i5 


69 


29 




3o 


25 


44 


i5 


90 


25 


37 


16 


01 


25 


3o 


16 


12 


25 


23 


16 


23 


3o 




3*1 


26 


29 


16 


43 


26 


22 


16 


54 


26 


i5 


16 


66 


26 


07 


16 


77 


3i 


1 


32 


27 


14 


16 


96 


27 


06 


17 


08 


26 


22 


17 


19 


26 


9i 


n 


3i 


32 




33 


27 


29 


n 


49 


27 


9 1 


17 


61 


27 


83 


n 


73 


27 


7 5 


17 


85 


33 




34 


28 


83 


18 


02 


28 


75 


18 


14 


28 


68 


18 


27 


28 


60 


18 


3 9 


34 




35 


29 


68 


18 


55 


29 


60 


18 


68 


29 


52 


18 


81 


29 


44 


18 


93 


35 




36 


3o 


53 


19 


08 


3o 


45 


J 9 


21 


3o 


36 


] 9 


34 


3o 


28 


*9 


48 


36 




37 


3i 


38 


x 9 


61 


3i 


29 


J 9 


74 


3i 


21 


19 


88 


3i 


12 


20 


02 


37 




38 


32 


23 


20 


i4 


32 


14 


20 


28 


32 


o5 


20 


42 


3i 


96 


20 


56 


38 


; 


3 9 


33 


07 


20 


67 


32 


98 


20 


81 


32 


89 


20 


9 5 


32 


80 


21 


10 


3 9 




4o 


33 


92 


21 


20 


33 


83 


21 


34 


33 


74 


21 


49 


33 


64 


21 


64 


40 




4i 


34 


77 


21 


73 


34 


67 


21 


88 


34 


58 


22 


o3 


34 


48 


22 


18 


4i 


1 


42 


35 


62 


22 


26 


35 


52 


22 


41 


35 


42 


22 


5 7 


35 


32 


22 


72 


42 


j 


43 


36 


47 


22 


79 


36 


37 


22 


9 5 


36 


27 


23 


10 


36 


16 


23 


26 


43 


; 


44 


37 


3i 


23 


32 


37 


21 


23 


48 


37 


11 


23 


64 


37 


01 


23 


80 


44 




45 


38 


16 


23 


85 


38 


06 


24 


01 


37 


o5 


24 


18 


37 


85 


24 


34 


45 


: ' 


46 


3 9 


01 


24 


38 


38 


90 


24 


55 


38 


80 


24 


72 


38 


69 


24 


88 


46 




47 


3 9 


86 


24 


9 1 


3 9 


75 


25 


08 


3 9 


64 


25 


25 


39 


53 


25 


43 


47 




48 


4o 


7i 


25 


44 


46 


5 9 


25 


61 


40 


48 


25 


79 


40 


37 


25 


97 


48 


i 


49 


4i 


55 


25 


97 


4i 


44 


26 


i5 


4i 


33 


26 


33 


4i 


21 


26 


5i 


49 




5o 


42-40 


26 -5o 


42-29 


26-68 


42-17 


26-86 


42-o5 


27 -o5 


5o 




o 

a 

at 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


09 

O 
S 
eg 


i 
















i 


Q 


5i 


J° 


57f° 


57 


h° 


57 


I;° 


Q 





Table 


IV. 


TRAVERSE TABLE. 




151 


g 
1 

3 
o 
p 


32° 


32|° 


m° 


32|° 


9 
& 

3 
O 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


43-25 


27 -o3 


43-i3 


27-21 


43-oi 


27.40 


42-89 


2709 


5i 


52 


44-io 


27-56 


43- 


98 


27- 


7 5 


43- 


86 


27- 


94 


43- 


73 


28 


i3 


52 


53 


44-95 


28-09 


44- 


82 


28- 


28 


44- 


70 


28- 


48 


44. 


58 


28 


67 


53 


54 


45-79 


28-62 


45- 


67 


28- 


82 


45- 


54 


29 


01 


45- 


42 


29 


21 


54 


55 


46-64 


29- 1 5 


46- 


5i 


29- 


35 


46- 


39 


29. 


55 


46- 


26 


29 


75 


55 


56 


47-49 


29-68 


47- 


36 


29. 


88 


47- 


23 


3o- 


09 


47- 


10 


3o 


o 9 


56 


57 


48-34 


30-21 


48- 


21 


3o- 


42 


48- 


07 


3o 


63 


47" 


94 


3o 


84 


57 


58 


49-19 


3o-74 


49 


o5 


3o- 


9 5 


48- 


92 


3i 


16 


48 


78 


3i 


38 


58 


5 9 


5o-o3 31-27 


49 


90 


3i- 


48 


4 9 - 


76 


3i 


70 


49 


62 


3i 


92 


5 9 


6o 


5o-88 


3i-8o 


5o- 


74 


32- 


02 


5o 


60 


32 


24 


5o 


46 


32 


46 


60 


6i 


Si- 73 


32-33 


8: 


59 


32- 


55 


5i> 


45 


32 


78 


5i 


3o 


33 


00 


61 


62 


52-58 


32-85 


44 


33- 


08 


52 


29 


33 


3i 


52 


14 


33 


54 


62 


63 


53-43 


33-38 


53- 


28 


33- 


62 


53 


i3 


33 


85 


52 


99 


34 


08 


63 


64 


54-28 


33-91 


54- 


i3 


34 


i5 


53 


98 


34 


39 


53 


83 


34 


62 


64 


65 


55-12 


34-44 


54 


97 


34 


68 


54 


82 


34 


92 


54 


67 


35 


16 


65 


66 


55-97 


34-97 


55 


82 


35 


22 


55 


66 


35 


46 


55 


5i 


35 


70 


66 


67 


56-82 


35-5o 


56 


66 


35 


7 5 


56 


5i 


36 


00 


56 


35 


36 


25 


67 


68 


57-67 


36-o3 


57 


5i 


36 


29 


57 


35 


36 


54 


57 


*9 


36 


79 


68 


69 


58-52 


36-56 


58 


36 


36 


82 


58 


J 9 


37 


07 


58 


o3 


37 


33 


69 


70 


5 9 -36 


37-09 


5 9 


20 


37 


35 


5 9 


04 


37 


61 


58 


87 


37 


87 


70 


7i 


60 -21 


37-62 


60 


o5 


37 


89 


59 


88 


38 


i5 


5 9 


7i 


38 


•4i 


7i 


72 


61 -06 


38-i5 


60 


89 


38 


42 


60 


72 


38 


69 


60 


55 


38 


•95 


72 


73 


61 -91 


38-68 


61 


74 


38 


9 5 


61 


5 7 


3 9 


22 


61 


4o 


3 9 


.49 


73 


74 


62-76 


39-21 


62 


58 


39 


49 


62 


41 


3 9 


76 


62 


24 


40 


■ o3 


74 


75 


63- 60 


39-74 


63 


43 


40 


02 


63 


25 


40 


3o 


63 


08 


4o 


57 


75 


76 


64-45 


40-27 


64 


28 


4o 


55 


64 


10 


4o 


83 


63 


92 


41 


• 11 


76 


77 


65- 3o 


4o- 80 


65 


12 


4i 


09 


64 


94 


41 


37 


64 


76 


4i 


•65 


77 


78 


66-i5 


41-33 


65 


97 


4i 


62 


65 


78 


4i 


9 1 


65 


60 


42 


•20 


78 


79 


67-00 


4i-86 


66 


81 


42 


16 


66 


63 


42 


45 


66 


■44 


42 


•74 


I 9 


80 


67-84 


42-39 


67 


66 


42 


69 


67 


47 


42 


98 


67 


■28 


43 


•28 


80 


81 


68-69 


42-92 


68 


5o 


43 


22 


68 


3i 


43 


52 


68 


•12 


43 


•82 


81 


82 


69-54 


43-45 


69 


35 


43 


76 


69 


16 


44 


06 


68 


•97 


44 


• 36 


82 


83 


70-39 


43-98 


70 


20 


44 


29 


70 


00 


44 


• 60 


69 


■81 


44 


•90 


83 


84 


71-24 


44-5i 


7 1 


04 


44 


82 


70 


84 


45 


-i3 


70 


•65 


45 


•44 


84 


85 


72-08 


45-o4 


7i 


89 


45 


36 


7i 


69 


45 


•67 


7* 


•49 


45 


•98 


85 


86 


72- 9 3 


45-57 


72 


73 


45 


89 


72 


53 


46 


21 


72 


• 33 


46 


• D2 


86 


8 


73.78 


46-10 


73 


58 


46 


42 


73 


38 


46 


■ 7 5 


73 


•H 


47 


•06 


87 


74-63 


46-63 


74 


42 


46 


96 


74 


22 


47 


• 28 


74 


• 01 


47 


•61 


88 


89 


75-48 


47-16 


75 


27 


47 


49 


75 


06 


47 


• 82 


74 


• 85 


48 


• i5 


89 


1 90 


•J6-32 


47-69 


76 


12 


48 


o3 


75 


9 1 


48 


• 36 


75 


.69 


48 


.69 


90 


9 1 


77.17 


48-22 


76 


96 


48 


56 


76 


7 5 


48 


.89 


76 


• 53 


49 


•23 


9 1 


92 


78-02 


48-75 


77 


•81 


49 


09 


77 


-5 9 


49 


• 43 


77 


• 38 


49 


•77 


92 


93 


78-87 


49-28 


78 


• 65 


49 


63 


78 


•44 


49 


•97 


78 


• 22 


5o 


• 3i 


9 3 


94 


79.72 


49-81 


79 


• 5o 


5o 


16 


79 


•28 


5o 


• 5i 


79 


• 06 


5o 


• 85 


9 i ' 


95 


80 -56 


5o-34 


80 


•34 


5o 


69 


80 


•12 


5i 


•04 


79 


• 90 


5i 


• 3 ? 


9 l 


96 


81 -4i 


50-87 


81 


• 19 


5i 


■23 


80 


•97 


5i 


• 58 


80 


•74 


5i 


.93 


96 


97 


82-26 


5i-4o 


82 


• 04 


5i 


•76 


81 


•81 


52 


•12 


81 


• 58 


52 


•47 


9 2 


98 


83-u 


5i -93 


82 


-88 


52 


•29 


82 


•65 


52 


•66 


82 


•42 


53 


•02 


98 


99 


83 -96 


52-46 


83 


•73 


52 


•83 


83 


•5o 


53 


•19 


83 


.26 


53 


• 56 


99 


100 


84-80 


52-99 


84-57 


53-36 


84-34 


53.73 


84-10 


54-io 


100 




a 
a 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


0) 



a 
«a 

a 


58° 


57|° 


57i° 


51\° 



152 






TRAVERSE TABLE. 


1 
Table IV. 


g 

a 
P 


33° 


33i° 


33i° 


33|° 


g 

£5" 

s 

? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


I 


0-84 


o-54 


0-84 


o-55 


0-83 


o-55 


o-83 


o-56 


I 


2 


1 


68 


1 


09 


1 


67 


1 


10 


1-67 


1 


10 


i-66 


1 


11 


2 


3 


2 


52 


1 


63 


2 


5i 


1 


64 


2-5o 


1 


66 


2-49 


1 


67 


3 


4 


3 


35 


2 


18 


3 


35 


2 


J 9 


3.34 


2 


21 


3-33 


2 


22 


4 


5 


4 


3 


2 


72 


4 


18 


2 


74 


4-17 


2 


76 


4-i6 


2 


78 


5 


6 


5 


3 


27 


5 


02 


3 


29 


5-oo 


3 


3i 


4-99 


3 


33 


6 


I 


5 


87 


3 


81 


5 


85 


3 


84 


5-84 


3 


86 


5-82 


3 


89 


I 


6 


71 


4 


36 


6 


§ 


4 


39 


6.67 


4 


42 


6-65 


4 


•44 


9 


7 


55 


4 


90 


7 


4 


9 3 


7-5o 


4 


97 


7-48 


5 


•00 


9 


10 


8 


3 9 


5 


45 


8 


36 


5 


48 


8-34 


5 


52 


8-3i 


5 


• 56 


10 


ii 


9 


23 


5 


99 


9 


20 


6 


o3 


9-17 


6 


07 


9-i5 


6 


■ ii 


11 


12 


10 


06 


6 


54 


10 


04 


6 


58 


10-01 


6 


62 


9-98 


6 


67 


12 


i3 


10 


90 


7 


08 


10 


87 


7 


i3 


10-84 


7 


18 


io-8i 


7 


■22 


i3 


14 


11 


74 


7 


62 


11 


7i 




68 


11-67 


I 


73 


11-64 


7 


.78 


14 


i5 


12 


58 


8 


n 


12 


54 


8 


22 


12 -5i 


28 


12-47 


8 


•33 


i5 


16 


i3 


42 


8 


71 


i3 


38 


8 


77 


i3-34 


8 


83 


i3-3o 


8 


•89 


16 


\l 


14 


26 


9 


26 


14 


22 


9 


32 


14-18 


9 


38 


i4-i3 


9 


•44 


H 


i5 


10 


9 


80 


i5 


o5 


9 


87 


i5-oi 


9 


9 3 


I4-Q7 


10 


•00 


18 


*9 


i5 


9 3 


10 


35 


i5 


89 


10 


42 


i5-84 


10 


49 


i5-8o 


10 


• 56 


l 9 


20 


16 


77 


10 


89 


16 


73 


10 


97 


16-68 


11 


04 


16-63 


11 


•11 


20 


21 


n 


61 


11 


44 


\l 


56 


11 


5i 


17 -5i 


11 


5 9 


17.46 


11 


.67 


21 


22 


18 


45 


n 


98 


40 


12 


06 


i8-35 


12 


14 


18-29 


12 


• 22 


22 


23 


*9 


29 


12 


53 


19 


23 


12 


61 


19-18 


12 


69 


19-12 


12 


.78 


23 


24 


20 


13 


i3 


07 


20 


07 


i3 


16 


20-01 


i3 


25 


19-96 


i3 


-33 


24 


25 


20 


97 


i3 


62 


20 


9 1 


i3 


7i 


20-85 


i3 


80 


20-79 


i3 


.89 


25 


26 


21 


81 


14 


16 


21 


74 


14 


26 


21-68 


14 


35 


21-62 


14 


•44 


26 


27 


22 


64 


14 


7 1 


22 


58 


14 


80 


22-5l 


14 


90 


22-45 


i5 


•00 


27 


28 


23- 


48 


i5 


25 


23 


42 


i5 


35 


23-35 


i5 


45 


23-28 


i5 


-56 


28 


2 9 


24" 


32 


i5 


79 


24 


20 


i5 


90 


24-18 


16 


01 


24-n 


16 


11 


29 


3o 


25- 


16 


16 


34 


25 


09 


16 


45 


25-02 


16 


56 


24-94 


16 


67 


3o 


3i 


26 


00 


16 


88 


25 


92 


l l 


00 


25-85 


J-7 


11 


25.78 


17 


22 


3i 


32 


26. 


84 


17 


43 


26 


76 


n 


55 


26-68 


17 


66 


26-61 


17 


78 


32 


33 


27. 


68 


17 


97 


27 


60 


18 


09 


27-52 


18 


21 


27-44 


18 


33 


33 


34 


28 


5i 


18 


52 


28 


43 


18 


64 


28-35 


18 


77 


28-27 


18 


89 


34 


35 


29 


35 


»9 


06 


29 


27 


l 9 


*9 


29.19 


l 9 


32 


29-10 


*9 


.44 


35 


36 


3o 


J 9 


l 9 


61 


3o 


11 


l 9 


74 


3o-02 


J 9 


87 


29-93 


20 


00 


36 


ll 


3i 


o3 


20 


i5 


3o 


94 


20 


29 


3o-85 


20 


42 


30-76 


20 


56 


3 7 


3i< 


87 


20 


70 


3i 


78 


20 


84 


31-69 


20 


97 


3i-6o 


21 


11 


38 


3 9 


32 


7i 


21 


24 


32 


62 


21 


38 


32-52 


21 


53 


32-43 


21 


67 


39 


4o 


33 


55 


21 


79 


33 


45 


21 


93 


33-36 


22 


08 


33-26 


22 


22 


40 


4i 


34 


3 9 


22 


33 


34 


29 


22 


48 


34-19 


22 


63 


34-09 


22 


78 


4i 


42 


35 


22 


22 


87 


35 


12 


23 


o3 


35-02 


23 


18 


34-92 


23 


33 


42 


43 


36 


06 


23 


42 


35 


96 


23 


58 


35-86 


23 


73 


35-75 


23 


89 


43 


. 44 


36 


90 


23 


96 


36 


80 


24 


12 


36 -69 


24 


29 


36-58 


24 


45 


44 


45 


37 


74 


24 


5i 


37 


63 


24 


67 


37-52 


24 


84 


37-42 


25 


00 


45 


46 


38 


58 


25 


o5 


38 


47 


25 


22 


38-36 


25 


39 


38-25 


25 


56 


46 ' 


47 


3 9 


42 


25 


60 


39 


3i 


25 


77 


39-19 


25 


94 


3 9 - 08 


26 


11 


47 


48 


4o 


26 


26 


14 


4o 


14 


26 


32 


40 -o3 


26 


49 


39.91 


26 


67 


48 


49 


4i 


09 


26 


69 


4o 


98 


26 


87 


4o-86 


27 


04 


40-74 


27. 


22 


49 


5o 


4i-93 


27-23 


41 -8i 


27-41 


41-69 


27.60 


4i-57 


27.78 


5o 





a 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


0> 


a 
S3 
□0 


5' 


1° 


56 


2.0 

4 


56i° 


56|° 



Table IV. 




TRAVERSE TABLE. 




153 


Distance. 


33° 


33*° 


38 


r 


33|° 


b 

B 
n 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


5i 


42.77 


27.78 


42-65 


27 -q6 


42-53 


28. i5 


42-40 


28-33 


5i 


52 


43-6i 


28 


•32 


43.49 


28 


• 5i 


43 


-36 


28 


■70 


43 


•24 


28 


-8 9 


52 


53 


44-45 


28 


.87 


44-32 


29 


■ 06 


44 


20 


29 


-25 


44 


• 07 


29 


•45 


53 


54 


43-29 


29 


•4i 


45.i6 


29 


■ 61 


45 


■ o3 


29 


• 80 


44 


• 90 


3o 


•00 


54 


55 


46- 13 


29 


.96 


46-00 


3o 


■ 16 


45 


■ 86 


3o 


• 36 


45 


■73 


3o 


•56 


55 


56 


46-97 


3o 


•DO 


46183 


3o 


• 70 


46 


• 70 


3o 


.91 


46 


56 


3i 


•11 


56 


57 


47-80 


3i 


•04 


47-67 


3i 


■25 


47 


•53 


3i 


-46 


47 


-3 9 


3i 


.67 


57 


58 


48-64 


3i 


• 5 9 


48 -5o 


3i 


.80 


48 


•37 


32 


•01 


48 


•23 


32 


•22 


58 


5 9 


49-48 


32 


■i3 


49-34 


32 


.35 


49 


•20 


32 


■ 56 


49 


■06 


32 


•78 


59 


6o 


5o-32 


32 


■ 68 


5o-i8 


32 


•90 


5o 


•o3 


33 


•12 


49 


89 


33 


• 33 


60 


6i 


5i-i6 


33 


22 


5i -oi 


33 


45 


5o 


87 


33 


.67 


5o 


•72 


33 


.89 


61 


62 


52-00 


33 


77 


5i-85 


33 


99 


5i 


• 70 


34 


• 22 


5i 


■ 55 


34 


•45 


62 


63 


52-84 


34 


3i 


52-69 


34 


54 


52 


53 


34 


•77 


52 


-38 


35 


•00 


63 


64 


53-6 7 


34 


86 


53-52 


35 


09 


53 


37 


35 


■32 


53 


21 


35 


56 


64 


65 


54-5i 


35 


40 


54-36 


35 


64 


54 


20 


35 


88 


54 


o5 


36 


•11 


65 


66 


55-35 


35 


9 5 


55- 19 


36 


l 9 


55 


04 


36 


43 


54 


88 


36 


67 


66 


u 


56-19 


36 


49 


56 -o3 


36 


74 


55 


87 


36 


98 


55 


71 


37 


• 22 


67 


57-o3 


37 


04 


56-87 


37 


28 


56 


70 


37 


53 


56 


54 


37 


.78 


68 


69 


5 7 -8 7 


37 


58 


57-70 


37 


83 


57 


54 


38 


08 


57 


37 


38 


-33 


69 


■70 


58-71 


38 


12 


58-54 


38 


38 


58 


37 


38 


64 


58 


20 


38 


89 


70 


71 


59.55 


38 


67 


5 9 -38 


38 


93 


5 9 


21 


3 9 


*9 


5 9 


o3 


3 9 


45 


71 


72 


6o-38 


39 


21 


60-21 


39 


48 


60 


04 


39 


74 


5 9 


87 


4o 


00 


72 


73 


6l -22 


39 


76 


61 -o5 


40 


o3 


60 


87 


40 


29 


60 


70 


4o 


56 


73 


74 


62-06 


4o 


3o 


61-89 


4o 


57 


61 


7i 


40 


84 


61 


53 


4i 


11 


74 


75 


62-90 


40 


85 


62-72 


41 


12 


62 


54 


4i 


4o 


62 


36 


4i 


67 


75 


76 


63-74 


4i 


39 


63-56 


41 


67 


63 


38 


41 


95 


63 


l 9 


42 


22 


76 


77 


64-58 


41 


94 


64- 3g 


42 


22 


64 


21 


42 


5o 


64 


02 


42 


78 


77 


78 


65-42 


42 


48 


65-23 


42 


77 


65 


04